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26richards · Dec 19, 2008, 06:40 AM

One person can do a page of problems in 10 minutes. Another person can dio the same problems in 20 minutes. If they both share the problems (ie. Not duplicating them), how fast can they complete the problems? I think the answer is 6 minutes and 40 seconds... but for the life of me (and I am 55 years old) I can't remember my junior high math.

ebaines · Dec 19, 2008, 08:54 AM

You are correct!

In doing problem like this where you are given "time to complete" data - here in minutes per page - you need to first convert to a rate in pages per minute. So you take the inverse of minutes per page to get pages per minute. You can then add the rates together to find the rate if both people work together, Then take the inverse of that to find the time to complete (in minutes per page):

$ T = \frac 1 { \frac 1 {T_1} + \frac 1 {T_2} + \frac 1 {T_3} + ...} $

So here you have:
$ T = \frac 1 {\frac 1 {10} + \frac 1 {20} } \\ = 20/3 \ minutes/page $

asking · Dec 19, 2008, 09:20 AM

One person can work at the rate of a tenth of a page per minute and the other person can work at the rate of a 20th page per minute.

How many minutes to complete one page?

X minutes (1/10 p/m + 1/20 p/m) = 1 page

Solve for X.

Then it looks just like what ebaines did above.