Question

Sam can mow a lawn in 40 minutes. Vanessa can mow the same lawn in 60 minutes. How long does it take for both Sam and Vanessa to mow the lawn if they are working together? Express your answer as a reduced fraction.

Answer 1

As a reduced fraction:
`(120)/(5)` minutes, which is 24 minutes

Explanation:

Sam's speed is 1 lawn in 40 minutes. Vanessa's speed is 1 lawn in 60 minutes. If they both work together, the total speed is:

`(1)/(40)+(1)/(60)=(1(3))/(40(3))+(1(2))/(60(2))=(3)/(120)+(2)/(120)=(5)/(120)`

Which means that the total speed would be 5 lawns in 120 minutes. To find the time it would take to mow one lawn at that speed, we need to invert that speed so we get minutes per lawn:

`(120)/(5)=24minutes`