alchemist009 wrote:

The third-place finisher of the Allen County hot dog eating contest, in which each contestant was given an equal amount of time to eat as many hot dogs as possible, required an average of 15 seconds to consume each hot dog. How many hot dogs did the winner eat?

(1) The winner consumed 24 more hot dogs than did the third-place finisher.

(2) The winner consumed hot dogs at double the rate of the third-place finisher.

The goal is to find the number of hot dogs that the winner ate. Incidentally, the average time per hot dog is not actually relevant to the problem.

Statement 1) W = T + 24

The winner ate 24 more hotdogs than the third place finisher. However, we don't know the value of either. Insufficient.

Statement 2) W = 2T. We know this fact is true because the time for each is the same. So if the winner has twice the rate of the third place finisher, then he did twice as much work (eating hot dogs) in the same amount of time. So he ate twice as many hotdogs. However, similar to statement 1, this statement is insufficient.

Statements 1+2) W = T + 24 and W = 2T.

Sufficient. We have two equations and two unknowns.