Question

Phyllis can rake our lawn in 50 min, and I can do it in 40 min. If she rakes for 5 min before I join her, how long will it take us to finish?

Answer 1

Think of this in terms of fractions of the lawn raked each minute.

Phyllis rakes 1/50 of the lawn per minute. You rake 1/40 of the lawn per minute. In 5 minutes, Phyllis rakes 5*1/50 = 1/10 of the lawn, leaving 9/10 to be raked. Combined, you and Phyllis rake
\[\frac{1}{40}+\frac{1}{50}\] of the lawn each minute. Divide 9/10 by that fraction to find the number of minutes of raking you will have to do together to complete raking the lawn.