Question

A runs \( 1 \frac{2}{3} \) times as fast as B. If A gives B a start of 80m, how far must the winning post be, so that A and B might reach it at the same time?

• A. 200 m
• B. 300 m
• C. 270 m
• D. 160 m

Hint:

Use relative speed concepts carefully in problems where one runner gives a head start to another.

Answer 1

The Correct Option is A

Let B’s speed be \( x \), then A’s speed is: \[ \frac{5}{3} x \] Let the total race distance be \( d \), and B runs \( d - 80 \) meters.
Since both finish at the same time: \[ \frac{d}{\frac{5}{3}x} = \frac{d - 80}{x} \] Cross multiplying: \[ 3d = 5(d - 80) \] \[ 3d = 5d - 400 \] \[ 2d = 400 \] \[ d = 200 \] Thus, the winning post must be 200 meters.