Question

A runs 5/3 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 at the same time.

Answer 1

200m is the answer.!

Answer 2

Winning post is at distance 200 m so that A and B reach at same time.

Solution:

The ratio of the speed of running of both A and B = $\frac{A}{B}=\frac{\frac{5}{3}}{1}=5 : 3$

Now as we can see that the total length of the race according to the ratio between their speeds is 5m, where is (5 – 3) is the distance by which A is at front of B.

Therefore, the distance at which the winning post should be situated from the start should be at  

$\bold{80\ m \times \frac{5}{2}=200\ m}$

The ratio 5 : 2 is the ratio of the total length upon the length by which A is ahead, therefore as seen in the question the distance by which A is ahead is 80 m, therefore multiplying it with the ratio 5 : 2 we get 200 m.