jmc

Question

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?

Accepted Answer

From the information given, we can set up the following equation: pt = (2p-4)(t-2). Simplifying this, we get pt - 4p - 4t = -8. Now, we can use Simon's Favorite Factoring Trick and add 16 to both sides to get pt - 4p - 4t + 16 = 8. This factors to (p-4)(t-4)=8Since p>10, the only possible combination of p and t is p=12 and t=5. Thus, I did a total of 12 5 = 60 problems.