Speed, Time and Distance - Quant/Math - CAT 2009
Question 4 the day:
April 28, 2003
The question for the day is from the topic of Speed, Time and Distance.
- 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?
| (1) |
545.45 metres |
| |
(2) |
666.67 metres |
| (3) |
857.14 metres |
| |
(4) |
Cannot be determined |
Correct Answer - (2)
Solution:
A and B run around a circular track. A laps B in the middle of the 5thlap. 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.
Which is the 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  = 666.67 metres.
The information with regard to the length of the circular track is redundant information.
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