Question

Fred can mow a lawn in 60 minutes. rocky can mow the same lawn in 40 minutes. how long does it take for both fred and rocky to mow the lawn if they are working together? express your answer as a reduced fraction.

Answer 1

24 minutes

Explanation:

Fred can mow a lawn in 60 minutes.

Fred's Rate
`=(1)/(60)`

Rocky can mow the same lawn in 40 minutes.

Rocky's rate
`=(1)/(40)`

Let the time it will take both of them = x minutes

Therefore:

`(1)/(60)+(1)/(40)=(1)/(x)\\$Multiply all through by 1200$\\1200* (1)/(60)+1200*(1)/(40)=1200*(1)/(x)\\20+30=(1200)/(x)\\50=(1200)/(x)\\$Cross multiply\\50x=1200\\Divide both sides by 50\\x=24\\`

It would take the two of them 24 minutes to mow the lawn.