● Ganita Prakash · Grade 8 · Chapter 3
Proportional Reasoning–2
Proportional Reasoning–2
— Full Solutions
Every Math Talk question and every Figure it Out exercise from the chapter, solved step-by-step — ratios with many terms, dividing a whole in a ratio, pie charts, and direct vs. inverse proportion, explained the way a Grade 8 student would work it out on paper.
3.1
Proportionality — A Quick Recap
From the textbook
Two ratios $a:b$ and $c:d$ are proportional if $a\times d = b\times c$, i.e. if $\dfrac{a}{c}=\dfrac{b}{d}$. We check this using cross-multiplication.
1
In-textViswanath mixes 6 cups rice with 3 cups urad dal (6 : 3). Puneet mixes 4 cups rice with 2 cups urad dal (4 : 2). If cooked the same way, would their idlis taste the same?
Answer
1
We need to check whether $6:3$ and $4:2$ are proportional, using cross-multiplication: check if $6\times2 = 3\times4$.
2
$6\times2 = 12$, and $3\times4=12$. Both products are equal.
3
Since the cross products match, the two ratios $6:3$ and $4:2$ are proportional (both simplify to $2:1$).
Yes — since $6:3$ and $4:2$ are proportional ratios (both equal to $2:1$), their idlis would taste the same, assuming all other ingredients are also kept in the same proportion.
3.2
Ratios in Maps
From the textbook
A Representative Fraction (RF) like $1:60{,}00{,}000$ means $1$ cm on the map equals $60{,}00{,}000$ cm of actual geographical distance.
2
In-textConvert 60,00,000 cm to kilometres. Verify that it is 60 km.
Answer
1
We know $1$ km $= 1000$ m, and $1$ m $=100$ cm. So $1$ km $= 1000\times100 = 1{,}00{,}000$ cm.
2
To convert $60{,}00{,}000$ cm to km, divide by $1{,}00{,}000$: $\dfrac{60{,}00{,}000}{1{,}00{,}000} = 60$.
$60{,}00{,}000$ cm $= 60$ km — verified. So $1$ cm on this map represents $60$ km on the ground.
3
In-textUsing the map (RF = 1 : 60,00,000), find the geographical distance between Bengaluru and Chennai, and between Mangaluru and Chennai.
Answer
1
From section 3.2, we found that on this map, $1$ cm represents $60$ km of real geographical distance.
2
Method: Use a ruler to measure the straight-line distance between the two city dots on the printed map (in cm), then multiply that measurement by $60$ km (since every 1 cm = 60 km).
3
On a typical printout of this map, Bengaluru and Chennai measure roughly $5$–$5.5$ cm apart, giving an estimated real distance of about $300$–$330$ km, which matches the actual geographical (straight-line) distance of approximately $290$ km between the two cities.
4
Mangaluru and Chennai are farther apart on the map, measuring roughly $7$–$7.5$ cm, giving an estimated distance of about $420$–$450$ km, close to the actual geographical distance of approximately $420$ km.
Bengaluru–Chennai ≈ 290–330 km, and Mangaluru–Chennai ≈ 420–450 km (your exact answer depends on your own ruler measurement on the printed map — multiply your cm reading by 60 to get km).
Since this is a “use a ruler on your own printed map” activity, your measured answer may vary slightly from these estimates — that’s expected and fine, as long as you multiplied correctly by the scale factor of 60.
4
In-textTry finding the distances between the same two pairs of cities using different maps with different scales. Do they all give approximately the same geographical distance?
Answer
1
Yes. Even though different maps may be drawn at different scales (say $1:50{,}00{,}000$ on one map and $1:60{,}00{,}000$ on another), the actual geographical distance between two fixed cities does not change.
2
A map with a smaller RF number (like $1:50{,}00{,}000$) will show cities farther apart on paper (since each cm represents fewer real km), while a map with a larger RF number (like $1:80{,}00{,}000$) will show them closer together on paper.
3
But when you multiply your ruler measurement by the correct scale factor for that specific map, you should land on approximately the same real-world distance each time — small differences are usually due to measurement error with the ruler, or the curvature of Earth not being captured exactly the same way on every map projection.
Yes — different maps with different scales should still give you approximately the same real geographical distance, since the actual distance between two cities is fixed; only the way it’s represented on paper changes.
3.3 / 3.4
Ratios with Multiple Terms & Dividing a Whole
From the textbook
A ratio can have more than 2 terms, like $8:4:2:1$. When two multi-term ratios are proportional, $a:b:c:d \;::\; p:q:r:s$, then $\dfrac{a}{p}=\dfrac{b}{q}=\dfrac{c}{r}=\dfrac{d}{s}$.
Key formula — dividing a quantity in a ratio
When dividing $x$ in the ratio $a:b:c:\ldots$, each part is:
$$x\times\dfrac{a}{(a+b+c+\ldots)},\quad x\times\dfrac{b}{(a+b+c+\ldots)},\quad x\times\dfrac{c}{(a+b+c+\ldots)},\ \ldots$$
5
In-textViswanath’s spice mix is coriander : chillies : toor dal : fenugreek :: 8 : 4 : 2 : 1. Puneet has only 2 red chillies. How much of the other ingredients should he use?
Answer
1
Viswanath used $4$ red chillies; Puneet has only $2$ — that’s $\dfrac{2}{4}=\dfrac12$ (half) the amount.
2
To keep the same taste (same ratio), every other ingredient must also be scaled down to half: coriander $8\times\frac12=4$ spoons, toor dal $2\times\frac12=1$ spoon, fenugreek $1\times\frac12=0.5$ spoon.
Puneet should use 4 spoons coriander, 2 chillies, 1 spoon toor dal, and 0.5 spoon fenugreek — giving the ratio $4:2:1:0.5$, which is proportional to Viswanath’s $8:4:2:1$.
6
In-text · Example 1Purple paint needs Red : Blue : White :: 2 : 3 : 5. With 10 litres of white paint, what is the total volume of purple paint made?
Answer
1
From the ratio, white corresponds to $5$ parts. Since $5$ parts $=10$ litres, $1$ part $=10\div5=2$ litres.
2
Red $=2$ parts $=2\times2=4$ litres. Blue $=3$ parts $=3\times2=6$ litres.
3
Total volume $=$ Red + Blue + White $= 4+6+10$.
Total volume of purple paint $= \mathbf{20}$ litres.
1
ExerciseA cricket coach divides a 150-minute session as warm-up/cool-down : batting : bowling : fielding :: 3 : 4 : 3 : 5. How much time is spent on each activity?
Answer
1
Add up the parts: $3+4+3+5=15$ parts total, representing $150$ minutes. So $1$ part $=150\div15=10$ minutes.
2
Warm-up/cool-down $=3\times10=30$ min. Batting $=4\times10=40$ min. Bowling $=3\times10=30$ min. Fielding $=5\times10=50$ min.
3
Check: $30+40+30+50=150$ ✓ minutes — matches the total session time.
Warm-up/cool-down: 30 min, Batting: 40 min, Bowling: 30 min, Fielding: 50 min.
2
ExerciseA library has Odiya : Hindi : English books :: 3 : 2 : 1. With 288 Odiya books, how many Hindi and English books are there?
Answer
1
Odiya books correspond to $3$ parts, and we’re told $3$ parts $=288$ books. So $1$ part $=288\div3=96$ books.
2
Hindi books $=2$ parts $=2\times96=192$ books. English books $=1$ part $=1\times96=96$ books.
The library has 192 Hindi books and 96 English books.
3
Exercise100 coins in the ratio ₹10 : ₹5 : ₹2 : ₹1 coins :: 4 : 3 : 2 : 1. How much money is there in total?
Answer
1
Total parts $=4+3+2+1=10$ parts, representing $100$ coins. So $1$ part $=100\div10=10$ coins.
2
Number of each coin: ₹10 coins $=4\times10=40$; ₹5 coins $=3\times10=30$; ₹2 coins $=2\times10=20$; ₹1 coins $=1\times10=10$.
3
Value contributed by each: $40\times₹10=₹400$; $30\times₹5=₹150$; $20\times₹2=₹40$; $10\times₹1=₹10$.
4
Total money $=400+150+40+10$.
Total money $= \mathbf{₹600}$.
4
Exercise · Math TalkConstruct a triangle with sidelengths in the ratio 3 : 4 : 5. Will all such triangles be congruent to each other?
Answer
1
A triangle with sides in ratio $3:4:5$ could have actual sides $3,4,5$ cm, or $6,8,10$ cm, or $30,40,50$ cm, or any other scaled-up version — the ratio only fixes the shape, not the size.
2
No, they will not all be congruent. Congruent triangles must have exactly equal corresponding sides, but triangles built from the same ratio can be scaled to any size.
3
However, all such triangles will be similar to each other — same shape, same angles, just different sizes.
No — triangles with sides in ratio $3:4:5$ are all similar (same angles), but not necessarily congruent, since the ratio doesn’t fix the actual size of the triangle.
5
ExerciseCan you construct a triangle with sidelengths in the ratio 1 : 3 : 5? Why or why not?
Answer
1
No, this is not possible. For any 3 lengths to form a triangle, they must satisfy the Triangle Inequality: the sum of any two sides must be greater than the third side.
2
Take sides in the ratio $1:3:5$ — say actual lengths $1, 3, 5$ units. Check: is $1+3 > 5$? That’s $4>5$, which is false.
3
Since the two shorter sides ($1$ and $3$) don’t add up to more than the longest side ($5$), they can never “meet” to close the triangle — they’d lie flat or fall short.
No — a triangle with sides in ratio $1:3:5$ cannot be constructed, because $1+3=4$ is not greater than $5$, violating the triangle inequality.
3.5
A Slice of the Pie
From the textbook
To draw a pie chart, divide the full circle’s $360°$ in the same ratio as the data. First simplify the ratio using HCF, then multiply each part by $\dfrac{360°}{\text{total parts}}$.
Worked example: Grades A,B,C,D,E in ratio 12:10:8:6:4 → simplified 6:5:4:3:2 → angles 108°,90°,72°,54°,36°
1
Exercise360 people voted for their favourite season: 90 liked summer, 120 liked rainy, and the rest liked winter. Draw a pie chart.
Answer
1
Winter $= 360 – 90 – 120 = 150$ people.
2
Since the total number of people is exactly $360$ — the same as the total degrees in a circle — we get a neat shortcut: each person’s vote corresponds to exactly $1°$. So the angle (in degrees) equals the number of people directly!
3
Summer $=90$ people $\to 90°$. Rainy $=120$ people $\to120°$. Winter $=150$ people $\to150°$.
4
Check: $90°+120°+150°=360°$ ✓ — exactly fills the circle.
Summer = 90°, Rainy = 120°, Winter = 150° — drawn as 3 slices that together make up the full circle.
2
ExerciseDraw a pie chart for TV channel preferences: Entertainment 50%, Sports 25%, News 15%, Information 10%.
Answer
1
Since these are percentages of a whole (which add up to $100\%$), we convert each percentage directly to degrees using: $\text{angle} = \dfrac{\text{percentage}}{100}\times360°$.
2
Entertainment: $\dfrac{50}{100}\times360°=180°$. Sports: $\dfrac{25}{100}\times360°=90°$.
3
News: $\dfrac{15}{100}\times360°=54°$. Information: $\dfrac{10}{100}\times360°=36°$.
4
Check: $180+90+54+36=360°$ ✓.
Entertainment = 180°, Sports = 90°, News = 54°, Information = 36°.
3
ExercisePrepare a pie chart showing the favourite subjects of students in your class.
Answer
1
This is a data-collection activity — you survey your own classmates and fill in the table with the actual number of students who chose each subject (Language, Arts Education, Vocational Education, Social Science, Physical Education, Maths, Science).
2
General method to follow once you have your numbers:
3
Add up all the student counts to get the class total, $N$.
4
For each subject, compute its angle using $\text{angle} = \dfrac{\text{number of students who chose it}}{N}\times360°$.
5
Draw a circle, mark a starting radius, and measure out each angle in turn (just like the Grade A–E example), labelling and colouring each slice.
Since this depends on your own class’s survey data, there’s no single fixed numeric answer — but once you have your counts, apply $\dfrac{\text{count}}{\text{total students}}\times360°$ to every subject, and the angles will always add up to exactly $360°$.
3.6
Inverse Proportions
From the textbook
Two quantities $x$ and $y$ are inversely proportional if $x\times y = k$ (a constant). As one increases by a factor $n$, the other decreases by the factor $\dfrac1n$ — unlike direct proportion, where both change the same way.
7
Math TalkPuneeth’s father rides a motorcycle (30 km/h, 3 hrs) vs. a car (60 km/h). Can we write this as $30:60::3:x$? Will travel time increase or decrease as speed increases?
Answer
1
No, we cannot use $30:60::3:x$ — that statement assumes direct proportionality (speed and time changing the same way), but that’s not what happens here.
2
As speed increases, the time taken to cover the same fixed distance decreases — they move in opposite directions. This is an inverse relationship, not a direct one.
3
The correct way to solve it: speed × time = distance (constant). So $30\times3 = 60\times x \Rightarrow 90=60x \Rightarrow x=1.5$.
Travel time will decrease as speed increases. With a car at 60 km/h, the trip would take 1.5 hours instead of 3.
8
In-textDoes travel time decrease by the same factor as speed increases, for all the modes of transport in the table (Walk 5 km/h–18 hrs, Bicycle 15 km/h–6 hrs, Motorcycle 30 km/h–3 hrs, Car 60 km/h–1.5 hrs)?
Answer
1
Compare Walk → Motorcycle: speed increases $30\div5=6$ times. Time decreases $18\div3=6$ times too. Same factor ✓
2
Compare Bicycle → Car: speed increases $60\div15=4$ times. Time decreases $6\div1.5=4$ times too. Same factor ✓
3
Compare Walk → Car: speed increases $60\div5=12$ times. Time decreases $18\div1.5=12$ times too. Same factor ✓
4
In every single case, $\text{speed}\times\text{time} = 90$ km (the fixed distance between Lucknow and Kanpur) — confirming the relationship is perfectly inverse.
Yes — in every case, the time decreases by exactly the same factor that the speed increases by, confirming these two quantities are inversely proportional (their product always equals 90 km).
1
ExerciseWhich of these tables show x and y in inverse proportion?
(i) x: 40,80,25,16 / y: 20,10,32,50 (ii) x: 40,80,25,16 / y: 20,10,12.5,8 (iii) x: 30,90,150,10 / y: 15,5,3,45
(i) x: 40,80,25,16 / y: 20,10,32,50 (ii) x: 40,80,25,16 / y: 20,10,12.5,8 (iii) x: 30,90,150,10 / y: 15,5,3,45
Answer
1
For inverse proportion, $x\times y$ must be the same constant for every pair in the table. Let’s check the product for each column:
| Table | Products $x\times y$ | Constant? |
|---|---|---|
| (i) | $40{\times}20{=}800$, $80{\times}10{=}800$, $25{\times}32{=}800$, $16{\times}50{=}800$ | ✅ Yes — all 800 |
| (ii) | $40{\times}20{=}800$, $80{\times}10{=}800$, $25{\times}12.5{=}312.5$, $16{\times}8{=}128$ | ❌ No — not constant |
| (iii) | $30{\times}15{=}450$, $90{\times}5{=}450$, $150{\times}3{=}450$, $10{\times}45{=}450$ | ✅ Yes — all 450 |
Tables (i) and (iii) show inverse proportion (constant product). Table (ii) does not, since the products aren’t all equal.
2
ExerciseFill in the empty cells if x and y are in inverse proportion: x: 16, 12, ___, 36 / y: 9, ___, 48, ___
Answer
1
First find the constant $k$ using the only complete pair: $x=16, y=9 \Rightarrow k=16\times9=144$.
2
For $x=12$: $y = \dfrac{144}{12}=12$.
3
For $y=48$: $x = \dfrac{144}{48}=3$.
4
For $x=36$: $y = \dfrac{144}{36}=4$.
| x | 16 | 12 | 3 | 36 |
|---|---|---|---|---|
| y | 9 | 12 | 48 | 4 |
Completed table: $x=16,12,3,36$ and $y=9,12,48,4$ — every pair multiplies to exactly $144$.
3.6
Inverse Proportions — More Worked Examples & Exercises
The two rules used throughout this section
Inverse proportion: $x_1y_1 = x_2y_2$ (product stays constant) | Direct proportion: $\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}$ (ratio stays constant)
From the textbook — Example 6 (Ram & Shyam cutting vegetables)
Ram finishes in 1 hour (so does 1 unit of work/hour). Shyam takes 1.5 hours (so does $\frac{1}{1.5}=\frac23$ unit/hour). Together they do $1+\frac23=\frac53$ units of work per hour. Since work and time are directly proportional, $\frac53:1::1:x \Rightarrow x=\frac35$ hour.
1
ExerciseWhich of these pairs are in inverse proportion? (i) taps & fill-time (ii) painters & days (iii) car distance & petrol (iv) cyclist speed & time (v) cloth length & price (vi) book pages & reading time
Answer
| Pair | Relationship | Type |
|---|---|---|
| (i) Taps & fill-time | More taps → less time to fill | Inverse |
| (ii) Painters & days | More painters → fewer days | Inverse |
| (iii) Distance & petrol | More petrol → more distance covered | Direct (not inverse) |
| (iv) Cyclist speed & time | More speed → less time for fixed route | Inverse |
| (v) Cloth length & price | More cloth → proportionally more cost | Direct (not inverse) |
| (vi) Book pages & reading time | More pages → proportionally more time | Direct (not inverse) |
Pairs (i), (ii), and (iv) are in inverse proportion. Pairs (iii), (v), (vi) are in direct proportion instead.
2
ExerciseIf 24 pencils cost ₹120, how much will 20 such pencils cost?
Answer
1
More pencils cost proportionally more money — this is a direct proportion. Set up: $24:120 :: 20:x$.
2
$x = \dfrac{20\times120}{24} = \dfrac{2400}{24}=100$.
20 pencils will cost ₹100.
3
Exercise · Math TalkA water tank supplies 20 families for 6 days. If 10 more families move in, how long will the water last? What assumptions are needed?
Answer
1
More families using the same fixed amount of water → the water lasts fewer days. This is an inverse proportion.
2
New number of families $=20+10=30$. Using $x_1y_1=x_2y_2$: $20\times6 = 30\times x \Rightarrow x=\dfrac{120}{30}=4$.
3
Assumptions needed: Every family uses water at the same daily rate, the tank’s total water supply is fixed (no extra refilling), and usage patterns don’t change (no extra wastage or saving).
The water will now last only 4 days.
4
ExerciseMatch each animal’s average daily sleep hours from this list: 15, 2.5, 20, 8, 3.5, 13, 10.5, 18.
Answer
1
This question asks you to match small pie-chart icons (showing “awake” vs “asleep” portions of a day) to the correct number of hours. Since the icons themselves can vary in print quality, here is the reasoning method, with typical real-world values for commonly used animals in this kind of chart:
| Typical animal | Approx. real sleep (hrs/day) | Closest value from list |
|---|---|---|
| Elephant | ~2 hrs | 2.5 |
| Giraffe / Horse | ~3–4 hrs | 3.5 |
| Human (child/adult) | ~8 hrs | 8 |
| Dog | ~10–11 hrs | 10.5 |
| Cat | ~12–16 hrs | 13 |
| Squirrel | ~14–15 hrs | 15 |
| Python / Armadillo | ~18 hrs | 18 |
| Bat / Opossum | ~19–20 hrs | 20 |
2
How to actually solve it from the pie icons in your book: for each small circular icon, estimate what fraction of the circle is shaded as “asleep.” Multiply that fraction by 24 (hours in a day) to estimate the sleep hours, then match it to the closest number in the given list.
The exact animal-to-icon matching depends on which 8 animals are pictured in your copy of the book, but using the method above — fraction of the circle shaded × 24 — you can match each icon to one of: 2.5, 3.5, 8, 10.5, 13, 15, 18, 20 hours.
Since the specific icons in this image are small line drawings that are hard to identify with full certainty, double check your matches against your textbook’s actual pictures — the method (shaded fraction × 24) is what matters most here.
5
ExercisePie chart of school transport: Walk 90°, Bus 120°, Cycle 60°, Two-wheeler 60°. (i) Most common mode? (ii) Fraction by car? (iii) If 18 travel by car, how many took the survey, and how many use taxis? (iv) Which two modes have equal numbers?
Reconstructed pie chart — Car’s angle is the remaining slice after the other 4 are subtracted from 360°
Answer
1
First, find Car’s angle. The given angles are Walk $90°$, Bus $120°$, Cycle $60°$, Two-wheeler $60°$. These add up to $90+120+60+60=330°$.
2
Since a full circle is $360°$, Car’s angle $=360-330=30°$.
3
(i) Most common mode: The largest angle is Bus at $120°$, so Bus is the most common mode of transport.
4
(ii) Fraction travelling by car: $\dfrac{30°}{360°} = \dfrac{1}{12}$.
5
(iii) Total surveyed: If $18$ children $=\frac{1}{12}$ of the total, then total $=18\times12=216$ children.
6
Regarding “how many use taxis” — this pie chart’s legend only lists Walk, Cycle, Bus, Two-wheeler, and Car; there’s no separate “Taxi” slice shown. So based on what’s actually in this chart, the answer is that taxi isn’t a category here — if your version of the chart does show a taxi slice, apply the same method: $\text{(taxi’s angle} \div 360°) \times 216$.
7
(iv) Equal numbers: Cycle ($60°$) and Two-wheeler ($60°$) have the same angle, so they represent equal numbers of children.
(i) Bus (ii) $\frac{1}{12}$ (iii) 216 children surveyed in total; no separate taxi category exists in this chart (iv) Cycle and Two-wheeler have equal numbers of children.
6
Exercise3 workers paint a fence in 4 days. If one more worker joins, how many days will it take? What assumptions are needed?
Answer
1
More workers → fewer days needed. This is inverse proportion. New number of workers $=3+1=4$.
2
$3\times4 = 4\times x \Rightarrow x=\dfrac{12}{4}=3$.
3
Assumptions: All workers work at the same speed/efficiency, they don’t get in each other’s way, and they all work the same number of hours per day.
It will take 3 days for 4 workers to finish the fence.
7
ExerciseA pump fills 2 tanks (same size) in 6 hours. How long will it take to fill 5 such tanks with the same pump?
Answer
1
More tanks to fill → proportionally more time needed. This is a direct proportion: tanks : time :: tanks : time.
2
Time for 1 tank $=6\div2=3$ hours. For $5$ tanks: $5\times3=15$ hours.
3
Or directly: $2:6::5:x \Rightarrow x=\dfrac{6\times5}{2}=15$.
It will take 15 hours to fill 5 tanks.
8
Exercise25 rows of 12 chairs are rearranged with 20 chairs per row. How many rows now?
Answer
1
Total number of chairs stays fixed $=25\times12=300$ chairs. More chairs per row → fewer rows needed — this is inverse proportion.
2
$25\times12 = 20\times x \Rightarrow x = \dfrac{300}{20}=15$.
The new arrangement has 15 rows.
9
ExerciseSchool has 8 periods of 45 minutes each. If it changes to 9 periods (same total school hours), how long is each period?
Answer
1
Total school time stays fixed $= 8\times45=360$ minutes. More periods → each period must be shorter — this is inverse proportion.
2
$8\times45 = 9\times x \Rightarrow x=\dfrac{360}{9}=40$.
Each period would now be 40 minutes long.
10
ExerciseA small pump fills a tank in 3 hours; a large pump in 2 hours. If both work together, how long will it take?
Answer
1
Think in terms of “tank per hour” rates. The small pump fills $\dfrac13$ of the tank per hour. The large pump fills $\dfrac12$ of the tank per hour.
2
Together, in 1 hour, they fill $\dfrac13+\dfrac12 = \dfrac{2}{6}+\dfrac{3}{6}=\dfrac56$ of the tank.
3
If $\dfrac56$ of the tank takes $1$ hour, then the whole tank (1 full tank) takes $1\div\dfrac56 = \dfrac65$ hours.
Together, the pumps will fill the tank in $\dfrac65$ hours $= \mathbf{1.2}$ hours (1 hour 12 minutes).
11
ExerciseA factory needs 42 machines to produce a batch of toys in 63 days. How many machines are needed to make the same batch in 54 days?
Answer
1
Fewer days available → need more machines working at once. This is inverse proportion.
2
$42\times63 = x\times54 \Rightarrow x=\dfrac{42\times63}{54} = \dfrac{2646}{54}=49$.
49 machines are needed to finish the same work in 54 days.
12
ExerciseA car takes 2 hours to reach a destination at 60 km/h. How long will it take at 80 km/h?
Answer
1
First find the fixed distance: $\text{distance} = \text{speed}\times\text{time} = 60\times2=120$ km.
2
Higher speed → less time for the same fixed distance. This is inverse proportion: $60\times2 = 80\times x \Rightarrow x=\dfrac{120}{80}=1.5$.
At 80 km/h, the car will take 1.5 hours (1 hour 30 minutes).
★
Quick Index — All In-text Questions
These are the Math Talk questions and in-text “?” prompts that appear directly inside the chapter’s explanations (not the end-of-section “Figure It Out” exercises). Tap any one to jump straight to its full solution above.
Solutions crafted for Grade 8 learners · Diagrams redrawn for clarity · @EDUGROWN