A student can answer a mathematical problem in 6 minutes, another two students can answer the same problem in 8 minutes and 10 minutes respectively. How long will it take the three students to answer the problem if all three work together.

Question

jamesj · Answer

The way to think about this problem and ones like it is rates:
- the first student solves problems at a rate of 1/6 of a problem per minute
- the other students solve 1/8th and 1/10th of a problem per minute.

Hence their combined rate of solving is
1/6 + 1/8 + 1/10 of a problem per minute.

And that is equal to
(20 + 15 + 12)/120 = 47/120 problems/minute.

Hence to solve one problem they need

120/47 minutes = 2.55 minutes