SOLUTION: Betty can mow a lawn in 40 minutes. Melissa can mow the same lawn in 20 minutes. How long does it take for both Betty and Melissa to mow the lawn if they are working together?

Question 960219: Betty can mow a lawn in 40 minutes. Melissa can mow the same lawn in 20 minutes. How long does it take for both Betty and Melissa to mow the lawn if they are working together?
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
Betty can mow a lawn in 40 minutes. Melissa can mow the same lawn in 20 minutes.
How long does it take for both Betty and Melissa to mow the lawn if they are
working together?

Since Betty can mow a lawn is 40 minutes, then
Betty's mowing rate is 1/40th of a lanw per minute.

Since Melissa can mow a lawn is 20 minutes, then
Melissa's mowing rate is 1/20th of a lawn per minute.

Suppose working together they can a lawn in x minutes

Since both together they can mow a lawn is x minutes, then
their combined mowing rate is 1/x th of a lawn per minute.

To get the equation, 

the sum of their mowing rates must equal their combined mowing rate,

1/40 + 1/20 = 1/x

Solve that by multiplying through by LCD of 40x and get x = 13 1/3 minutes.

Edwin

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