SOLUTION: Twin brothers, person A and person B can mow their parents lawn together in 72 minutes. Person B could mow the lawn by himself in 17 minutes more than it would take person A. How l

Question 686876: Twin brothers, person A and person B can mow their parents lawn together in 72 minutes. Person B could mow the lawn by himself in 17 minutes more than it would take person A. How long would it take each alone? The person who can solve this right first I will buy them lunch.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Twin brothers, person A and person B can mow their parents lawn together in 72 minutes. Person B could mow the lawn by himself in 17 minutes more than it would take person A. How long would it take each alone?
**
let x=time it takes person A to mow the lawn alone
his work rate=1/x
x+17=time it takes person B to mow the lawn alone
his work rate=1/(x+17)
72 minutes=time it takes persons A and B to mow the lawn together
their work rate=1/72
sum of individual work rates=work rate working together
1/x+1/(x+17)=1/72
LCD:72x(x+17)
72(x+17)+72x=x(x+17)
72x+1224+72x=x^2+17x
144x+1224=x^2+17x
x^2-127x-1224=0
factor:
(x+9)(x-136)=0
x=-9(reject)
or
x=136
x+17=153
...
time it takes person A to mow the lawn alone=136 min
time it takes person B to mow the lawn alone=153 min

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