In a 100 m race, A finishes while B is still 15 m short. We say A beats B by 15 m. Is A 15% faster? No. A runs 100 m while B runs 85 m, so the speed ratio is 20 : 17.
This article shows how to read race language, the shortcuts, and five solved examples. Each one says why the method works.
- Speed: distance ÷ time.
- A beats B by d: when A finishes, B is d metres short.
- A gives B a start of s: B runs s metres less.
- Same time: speed ratio = distance ratio.
- Beats by d metres or t seconds: B’s speed is d ÷ t.
- Chains: multiply the distance ratios.
- Dead heat: all runners finish together.
How do you read the language of races?
What does speed mean in a race?
Speed is the distance covered in one unit of time. So speed = distance ÷ time.
A runner who covers 400 m in 100 s runs at 4 m per second.
Sources: NCERT Class 7 Science: Motion and Time, speed as distance over time.
Which runner is faster?
The runner who covers more distance in the same time is faster. Or the runner who needs less time for the same distance.
So to compare runners, fix either the time or the distance.
Sources: NCERT Class 7 Science: Motion and Time, faster and slower; Practice question: speed ratio in a 100 m race.
What does ‘A beats B by 15 m’ mean?
When A reaches the finish line, B is still 15 m short. So B has run only 85 m of a 100 m race.
The gap is measured at the moment A finishes.
Sources: NCERT Class 7 Science: Motion and Time, using speed to compare.
What does ‘A gives B a start of 20 m’ mean?
B starts 20 m ahead. So B runs 20 m less than A.
If the race is 100 m long, A runs 100 m and B runs 80 m.
Sources: NCERT Class 7 Science: Motion and Time, unit of speed.
What is a dead heat?
A dead heat is a race where all runners reach the finish line at exactly the same time.
In this case, the speed ratio equals the ratio of the distances they run.
Sources: NCERT Class 7 Science: Motion and Time, equal times for two objects.
Which shortcuts make race problems quick?
How do you find the speed ratio?
Run the same time. So speed ratio = distance ratio.
If A runs 100 m while B runs 85 m, A : B = 100 : 85 = 20 : 17.
Sources: NCERT Class 7 Science: Motion and Time, total distance and total time; Practice question: 20 : 17 speed ratio.
How do you find the length of the race from a start?
Say A is p/q times as fast as B. If A gives a start of s metres, then d = s × p ÷ (p − q).
For speeds 4/3 and a start of 20 m, d = 20 × 4 ÷ 1 = 80 m.
How do you find a runner’s time from ‘beats by d metres or t seconds’?
The slower runner covers d metres in t seconds. So the slower speed is d ÷ t.
Then the winner’s time equals the slower runner’s time over the distance he actually ran.
Sources: NCERT Class 7 Science: Motion and Time, finding time from speed; Practice question: Neha’s time in a 500 m race.
How do you find by how much one runner beats another from their times?
Take the winner’s time. Find how far the slower runner goes in that time. The gap is the margin.
If Neha takes 70 s for 800 m and Priya takes 100 s, Priya runs 560 m in 70 s. So Neha beats her by 240 m.
Sources: NCERT Class 7 Science: Motion and Time, finding distance from speed; Practice question: Neha and Priya over 800 m.
How do you handle three runners?
Chain the ratios. Multiply the distance ratios of A to B and B to C.
If A beats B by 15 m and B beats C by 20 m in 100 m, A beats C by 32 m.
How do you find a start between two others?
Convert each start to a ratio of distances in the same race. Then divide.
If Neha gives Divya 250 m and Rohan 298 m in 1000 m, then Divya : Rohan = 750 : 702. So Divya gives Rohan 64 m.
What are games of skill?
In a game of 120 points, if Rohan can give Meera 7 points, Meera starts at 7. When Rohan scores 120, Meera scores 113.
The idea is the same as a start in a race.
Sources: Practice question: game of 120 points.
Check 1
If A beats B by 15 m in 100 m, the speed ratio A : B is 20 : 17.
Check 2
If A beats B by 15 m, A is 15% faster.
Check 3
A start of 20 m means B runs 20 m less.
Check 4
The gap is measured when B finishes.
How do you solve five typical problems step by step?
Example 1: In a 200 m race, A beats B by 40 m. Find the speed ratio.
Step 1. When A runs 200 m, B runs 200 − 40 = 160 m.
Step 2. The speed ratio is 200 : 160.
Step 3. Divide by 40: 5 : 4.
Check. 5 × 40 = 200 and 4 × 40 = 160.
Why this works. Both runners run for the same time. So distances compare like speeds.
Sources: Practice question: speed ratio.
Example 2: A is 5/3 times as fast as B. A gives B a start of 40 m. How long is the race?
Step 1. Let the race be d metres. A runs d. B runs d − 40.
Step 2. d ÷ (d − 40) = 5/3. So 3d = 5d − 200.
Step 3. So 2d = 200, and d = 100 m.
Check. A runs 100 m. B runs 60 m. 100 : 60 = 5 : 3.
Why this works. The start makes up exactly the gap in distance.
Sources: Worked check: race length from a start.
Example 3: In a 300 m race, A beats B by 30 m or 6 seconds. Find A’s time.
Step 1. B covers 30 m in 6 s. So B’s speed is 5 m/s.
Step 2. B ran 300 − 30 = 270 m while A ran 300 m.
Step 3. B takes 270 ÷ 5 = 54 s for that. So A’s time is 54 seconds.
Check. A’s speed is 300 ÷ 54 = 50/9 m/s. B at 5 m/s takes 60 s for 300 m, which is 6 s more.
Why this works. When A finishes, B has run for the same time as A.
Sources: Worked check: time from a gap.
Example 4: A runs 600 m in 80 s. B runs it in 100 s. By how much does A win?
Step 1. B’s speed is 600 ÷ 100 = 6 m/s.
Step 2. In 80 s, B covers 6 × 80 = 480 m.
Step 3. A wins by 600 − 480 = 120 m.
Check. 80 : 100 = 4 : 5, and 480 : 600 = 4 : 5.
Why this works. We freeze the race at the moment A finishes.
Sources: Worked check: margin from times.
Example 5: A beats B by 20 m, and B beats C by 10 m, in a 100 m race. By how much does A beat C?
Step 1. When A runs 100 m, B runs 80 m.
Step 2. When B runs 100 m, C runs 90 m. So when B runs 80 m, C runs 0.9 × 80 = 72 m.
Step 3. A beats C by 100 − 72 = 28 m.
Check. The ratio is 100 : 80 : 72, so A : C = 100 : 72.
Why this works. Each runner’s distance is a fixed fraction of the one before.
Sources: Worked check: three runners in a chain.
How do you avoid careless mistakes?
What habits keep answers right?
Draw the finish line. Mark where each runner stands when the winner finishes.
Keep the race length fixed. Compare distances, not gaps.
Check 5
A beats B by 15 m means A runs 15 m more than B in the whole race.
Check 6
A start of 12 m in a 100 m race means B runs 88 m.
Exam traps
Gap trap. The gap is measured when the winner finishes, not when the loser does.
Start trap. A start helps the slower runner. The faster runner runs the full distance.
Percent trap. A 15 m gap in 100 m is not 15% faster. Use the 100 : 85 ratio.
Chain trap. Multiply ratios. Do not add the gaps.
Unit trap. Convert minutes and seconds to seconds first.
MCQ on Races and Games of Skill
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