SOLUTION: Peter mows a lawn in 40 minutes. John moes the lawn in 60 minutes. How long will it take them to mow the lawn together?

Question 165332: Peter mows a lawn in 40 minutes. John moes the lawn in 60 minutes. How long will it take them to mow the lawn together?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Peter mows a lawn in 40 minutes. John moes the lawn in 60 minutes. How long will it take them to mow the lawn together?
Let x=amount of time it takes both working together to mow the lawn
Together, they work at the rate of 1/x lawn per hour
Peter works at the rate of 40/60=2/3 lawn per hour
John works at the rate of 1 lawn per hour
Together, they work at the rate of 2/3 + 1=1 2/3 =5/3 lawns per hour
So, our equation to solve is:
(5/3)*x=1 (1 lawn, that is) multiply each term by 3
5x=3 divide both sides by 5
x=3/5 hour=36 min
Another way:
2/3 +1=1/x
5/3=1/x multiply each term by 3x
5x=3
x=3/5
CK
Peter:
(2/3)*(3/5)=2/5 lawn
John:
1*(3/5)=3/5 lawn
2/5 + 3/5=1
1=1
Hope this helps---ptaylor

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