A runs 3 times as fast as B. If A gives B a start of 30 meters, how far must the goal on the race course be so that A and B reach it at the same time?

45 m

The correct answer is Option (3) → 45 m

A runs 3 times as fast as B.

Let speed of B = $v$ Speed of A = $3v$

If A gives B a start of 30 m, then:

A runs a distance = $D$ B runs a distance = $D - 30$

They finish at the same time:

$\frac{D}{3v} = \frac{D - 30}{v}$

Multiply both sides by $3v$:

$D = 3(D - 30)$

$D = 3D - 90$

$2D = 90$

$D = 45$

The goal must be 45 meters away.