In a race of 500 m run, A beats B by 20 m and C by 80 m. If B and C are…
2024
In a race of 500 m run, A beats B by 20 m and C by 80 m. If B and C are running another race of 100 m with exactly same speed as before, then by how many meters will B beat C?
- A.
10.0 m
- B.
8.5 m
- C.
15.0 m
- D.
12.5 m
Attempted by 19 students.
Show answer & explanation
Correct answer: D
Key idea: find speed ratios from the 500 m races and use them to see how far C runs when B finishes 100 m.
From A beats B by 20 m in a 500 m race: when A has run 500 m, B has run 480 m. So vA : vB = 500 : 480 = 25 : 24.
From A beats C by 80 m in a 500 m race: when A has run 500 m, C has run 420 m. So vA : vC = 500 : 420 = 25 : 21.
Compute the ratio vC/vB using the two results: vC/vB = (vC/vA) ÷ (vB/vA) = (21/25) ÷ (24/25) = 21/24 = 7/8.
When B runs 100 m, the distance C runs in the same time = 100 × (vC/vB) = 100 × 7/8 = 87.5 m.
Therefore B beats C by 100 - 87.5 = 12.5 m.
Answer: B beats C by 12.5 m.