Wilma can mow a lawn in 80 minutes. Melissa can mow the same lawn in 40 minutes. How long does it take for both Wilma and Melissa to mow the lawn if they are working together? Express your answer as a reduced fraction.

It takes them approximately 27 minutes to mow the lawn if they are working together.

Step-by-step explanation:

Wilma can mow a lawn in 80 minutes. This means she can mow at the rate of 1 lawn in 80 minutes. We can write this rate as R = 1/80

Melissa can mow the same lawn in 40 minutes. This means she can mow at the rate of 1 lawn in 40 minutes. We write the rate as R = 1/40.

Now, if the are working together, we need to determine how long it would take for them to mow a lawn. Let this rate be 1/x.

What we want to find is

1/80 + 1/40 = 1/x

Multiply through by 80, we have

1 + 2 = 80/x

3 = 80/x

Take reciprocals of both sides

x/80 = 1/3

x = 80/3

= 1600 seconds

Approximately 27 minutes