Question

Shelly can cut a lawn with a riding mower in 22 hours less time than it takes william to cut the lawn with a push mower. if they can cut the lawn in 33 hours working together find how long to the nearest tenth of an hour it takes for william to cut the lawn alone.

Answer 1

Let n be the amount of time it takes william to cut the lawn. Then Shelly takes
n-2 hours. So:
1/n+1/n-2=1/3
3(n-2)+3n=n²-2n
6n-6=n²-2n
n²-8n+6=0
Using the quadratic formula, we get a positive value of 7.1623 hrs as the amount of time william takes working alone, and 5.1623 as the amount of time Shelly takes working alone
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