Question

A runs 7/4 times as fast as
b. If a gives b a start of 90 m, how far must the winning post be so that a and b might reach it at the same time

Answer 1

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If A runs 7/4 times as fast as B

⇒ A : B = 7 : 4

Let x be the constant ratio

A : B = 7x : 4x

The difference is 90m

7x - 4x = 90

3x = 90

x = 30m

The winning post is the distance A has to run

= 7x = 7(30) = 210 m

Answer: The winning post has to be 210 m away.

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Answer 2

Once you see that A gains 3 metres over B in a 7-metre race, the question becomes: by how much must we scale the 7-metre race to compensate for the 84-metre head start?

If the race is 7k metres long, A will gain 3k metres. We want to find 7k, given that 3k=84. Thus 7k=7(843)=196.