A’s speed is 30/17 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?
Choose the correct choice from the following answers.
A) 1/17	B) 13/30	C) 17/30	D) 11/30	E) 11/13
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 30 meters, B covers 17 meters in that time. So if the race is 30 meters long, when A reaches the finish line, B would be 13 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 13 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 30 meters) would be the same as the time required by B (to cover 17 meters) to reach the finish line.   So B should get a head start of 13/30th of the race.   Answer (13/30)
<result>B</result>
A’s speed is 30/17 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?