A’s speed is 51/44 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.
A) 1/51	B) 4/51	C) 7/51	D) 3/44	E) 7/44
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 51 meters, B covers 44 meters in that time. So if the race is 51 meters long, when A reaches the finish line, B would be 7 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 7 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 51 meters) would be the same as the time required by B (to cover 44 meters) to reach the finish line.   So B should get a head start of 7/51th of the race.   Answer (7/51)
<result>C</result>
A’s speed is 51/44 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?