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Linear & Circular Races · Topic 4 of 5

⚡ Find Speed from the Race

2 exam question types, fully solved

Here the race outcome is given and you work backwards to a speed, a track length, or the time someone took. The key is that in the same time, distance is proportional to speed — so a ratio of distances is a ratio of speeds.

Same time ⇒ distance ratio = speed ratio

• When A finishes a race of length and beats B by m, both ran for the same time, so . Knowing one speed gives the other.

• Chained beats. If A beats B and B beats C, multiply the ratios: , then read off by how much A beats C.

• Speed swap at the meeting point. Two runners start toward each other; after meeting, A takes to reach the far end and B takes . Then — the square-root rule.

🏃Linear Race SimulatorAnimate the race
AB
A: 0.0 mB: 0.0 mResult: A wins by 20.0 m = 2.5 s

In a 100 m race A beats B by 20 m. The speed ratio .

📝Practice Questions

Q1A runs 100 m in 10 s; B in 12 s. By how many metres does A beat B?

Q2Two run at 50 m/min and 60 m/min; the faster finishes 5 min sooner. Race length:

Q3Two go opposite ways on a 600 m loop and exchange speeds when they first meet. They return to the start:

📚

Real exam questions — Find Speed from the Race

2 question types · 6 solved examples from real SSC papers

Read the outcome backwards: a beat is a time-gap-to-distance conversion, "finishes sooner" is a time-difference equation, and a speed swap on a loop has a tidy "both arrive together" answer.

How to solve this type
Every clue is really a statement about equal time or a time gap. Pin down what is shared and write one clean equation.

• Time gap from a beat: the loser's speed times the WINNER's time tells you where the loser had reached; the rest of the track is the beat. (Beat =time gaploser’s time×d=\dfrac{\text{time gap}}{\text{loser's time}}\times d.)
• "Finishes tt minutes sooner": set dv<sub>slow</sub>−dv<sub>fast</sub>=t\dfrac{d}{v<sub>\text{slow</sub>}}-\dfrac{d}{v<sub>\text{fast</sub>}}=t and solve for dd.
Keep units consistent and convert m/s ↔\leftrightarrow km/h with the 518\dfrac{5}{18} / 185\dfrac{18}{5} factors.

A runs a 200 m race in 25 s; B finishes the same race in 30 s. By how many metres does A beat B?

A33.33 mB30 mC32 mD33 m

Rahul runs 100 m at 6 km/h, gives Bharat a 4 m start and beats him by 4 s. Find Bharat's speed.

A4.9 km/hB5.8 km/hC5.4 km/hD4.5 km/h

Two racers run at 100 m/min and 120 m/min. The faster one finishes 10 minutes sooner. How long is the race?

A4 kmB2 kmC6 kmD1 km