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John can mow a lawn in 80 minutes. Rocky can mow the same lawn in 120 minutes. How long does it take for both John and Rocky to mow the lawn

Home/Math/John can mow a lawn in 80 minutes. Rocky can mow the same lawn in 120 minutes. How long does it take for both John and Rocky to mow the lawn

John can mow a lawn in 80 minutes. Rocky can mow the same lawn in 120 minutes. How long does it take for both John and Rocky to mow the lawn

Question

John can mow a lawn in 80 minutes. Rocky can mow the same lawn in 120 minutes. How long does it take for both John and Rocky to mow the lawn if they are working together?

## Answers ( )

Answer: it will take them 48 minutes.

Step-by-step explanation:

John can mow a lawn in 80 minutes. This means that the rate at which he moans the lawn per minute is 1/80

Rocky can mow the same lawn in 120 minutes. This means that the rate at which Rocky can mow the same lawn per minute is 1/120

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined working rate would be

1/80 + 1/120 = 200/9600 = 1/48

Assuming it takes t hours for both of them to clean the room working together, the working rate per hour would be 1/t. Therefore,

1/48 = 1/t

t = 48 minutes