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?
Answer & explanation
Correct answer: option 3
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.