Two cyclists, who weigh the same and have identical bicycles, ride up the same m

Question

Two cyclists, who weigh the same and have identical bicycles, ride up the same mountain, both starting at the same time. Joe rides straight up the mountain, and Bob rides up the longer road that has a lower grade. Joe gets to the top before Bob. Which statement is true?

A) Ignoring friction and wind resistance, Bob and Joe exerted the same amount of work, and the average power of each cyclist was also the same.

B) Ignoring friction and wind resistance, the amount of work done by Joe is greater than the amount of work done by Bob, and the average power exerted by Joe is greater than that of Bob.

C) Ignoring friction and wind resistance, the amount of work done by Joe is equal to the amount of work done by Bob, but the average power exerted by Joe is greater than that of Bob.

D) ) Ignoring friction and wind resistance, the average power exerted by Bob and Joe was the same, but Joe exerted more work in getting there.

I already know the answer is C, but I do not understand why. Please explain mathematically

Explanation / Answer

C) is the correct answer as in both case work = mgh that is same, but Power = work / time.
Time is taken less by Joe, So Joe's power was greater.

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