Question

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.

Answer 1

Third placer consumed 24 hot dogs.

Winner consumed 48 hot dogs.

Explanation:

Lets assume that the third runner up eats x hot dogs.

The total time for the contest is 15x seconds.

Given is that the winner ate (x+24) hot dogs

The winner's rate of eating is 1 hot dog per 7.5 seconds.

And we know the rate =
`(totaltime)/(number of hot dogs eaten)`

We get;

`(15x)/(x+24) =7.5`

`(x+24)7.5=15x`

`7.5x+180=15x`

`7.5x=180`

x = 24 (third placer)

And the winner consumed
`24+24=48` hot dogs.