A’s speed is 16/15 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 option
A) 1/8  B) 1/16  C) 1/15  D) 1/32  E) 1/31
Let x be the fraction of the distance that B runs.   Let v be the speed at which B runs.   The time should be the same for both runners.   Time = D / (16v/15) = xD/v   (15/16)*D/v = x*D/v   x = 15/16   B should have a head start of 1/16 of the full distance.   The answer is 1/16.
<result>B</result>
A’s speed is 16/15 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?