400
Two friends A and B run around a circular track of length 510 metres, starting from the same point, simultaneously and in the same direction. A who runs faster laps B in the middle of the 5th round. If A and B were to run a 3 km race long race, how much start, in terms of distance, should A give B so that they finish the race in a dead heat?
A.
545.45 metres
B.
666.67 metres
C.
857.14 metres
D.
Cannot be determined
Answer – (B)
Solution:
A and B run around a circular track. A laps B in the middle of the 5th lap. i.e. when A has run four and a half laps he has covered a distance which is 1 lap greater than that covered by B's.
Therefore, when A runs
9
2
laps, B runs
7
2
laps.
This is same as saying when A runs 9 laps, B runs 7 laps.
i.e in a race that is 9 laps long, A can give B a start of 2 laps.
So, if the race is of 3000 metres long, then A can give B a start of (
2
9
)×3000= 666.67 metres.
The information with regard to the length of the circular track is redundant information.