Mahesh Godavarti

These types of problems are rate problems.

The assumption here is that the rates add up.

If the rate of writing recommendation letters for Bob is A and for Bill is B, then the combined rate for both Bob and Bill is A + B.  Why? This can be explained as follows. If Bob write A letters per hour and Bill write B letters per hour, then together they will write A + B letters per hour.

So, the steps are:

  1. Use the information to calculate A, which is 2/4 = 1/2 a letter per hour
  2. Use the information to calculate B, which is 2/6 - 1/3 a letter per hour
  3. Calculate the combined rate = 1/2 + 1/3 = 5/6 letter per hour
  4. Use the combined rate to find the time = 6 / (5/6) = 36/5 = 7 1/5 hours = 7 hours and 12 minutes

This approach will work all types of problems that are similar to this.