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? Choices
A) 1 / 51
B) 4 / 51
C) 7 / 51
D) 3 / 44
E) 7 / 44

Rationale: "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 / 51 th of the race . answer ( c )"
Answer: C