A’s speed is 32/27 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?  Select the correct option
A) 5/32	B) 5/27	C) 1/27	D) 1/32	E) 27/32
We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.   This is what the beginning of the race will look like:   (Start) A_________B______________________________   If A covers 32 meters, B covers 27 meters in that time. So if the race is 32 meters long, when A reaches the finish line, B would be 5 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 5 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 32 meters) would be the same as the time required by B (to cover 27 meters) to reach the finish line.   So B should get a head start of 5/32 th of the race.   5/32nswer (5/32)
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A’s speed is 32/27 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?