My friend and i both have the same math homework one day. i work at a rate of $p$ problems per hour and it takes me $t$ hours to finish my homework. my friend works at a rate of $2p-4$ problems per hour and it only takes him $t-2$ hours to finish his homework. given that $p$ and $t$ are positive whole numbers and i do more than $10$ problems per hour, how many problems did i do?

If you do problems per hour, after hours you do problems.

Similarly, your friend does problems per hour, so after he has completed problems.

Since you have the same number of problems, we deduce

which we can rewrite as

If we solve this equation for one of the two variables, for example t, we have

Since p and t are positive integers, p must be at least 4.

Finding integers solutions require a bit of trial and error, and you can figure out that the only positive and integer solution where p > 10 is

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d