Question

The ratio of the average speeds of two sprinters A and B is 8:7. In a racing track if B starts at a distance 2m
ahead of A. at what distance (in metre) from the starting point of B would A catch up with B?​

Answer 1

Given :- The ratio of the average speeds of two sprinters A and B is 8:7. In a racing track , if B starts at a distance 2m ahead of A. at what distance (in metre) from the starting point of B would A catch up with B ?

Solution :-

As we know that,

• A gives a start of x metres to B implies if A starts the race from starting point, then B starts x metres ahead of A. To cover race of 100 metres in this case, A will have to cover 100 metres while B will have to cover only (100 - x) metres.

• They meet for the first time on the circular track (not necessarily at the starting point) = Length of the track / Relative Speed .

So, Let us assume that, Speed of A is 8x m / sec. and speed of B is 7x m / sec.

Now, we have given that, B starts at a distance of 2m ahead of A .

we can say that, A has have to cover this 2m distance in order to catch B .

So,

→ Distance = 2m .

→ Usual speed = (8x - 7x) = x m/sec. { same direction. }

Than,

→ Time taken by A to catch/meet B = Distance covered / usual speed = (2/x) seconds.

Therefore,

→ in (2/x) seconds A covered = Speed * Time = 8x * (2/x) = 16m.

Hence,

→ Distance (in metre) from the starting point of B would A catch up with B is = 16 - 2 = 14 m (Ans.)

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