SOLUTION: Twin​ brothers, Billy and​ Bobby, can mow their​ grandparent's lawn together in 63 minutes. Billy could mow the lawn by himself in 30 minutes less time that it would take Bo

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Question 1174770: Twin​ brothers, Billy and​ Bobby, can mow their​ grandparent's lawn together in 63 minutes. Billy could mow the lawn by himself in 30 minutes less time that it would take Bobby. How long would it take Bobby to mow the lawn by​ himself?
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
Bobby's rate of work = 1%2Fx of the lawn per minute
Billy's rate of work = 1%2F%28x-30%29 of the lawn per minute

Rate of work working together = 1%2Fx + 1%2F%28x-30%29 = 1%2F63

Solve for x:

1%2Fx + 1%2F%28x-30%29 = 1%2F63

%28x-30%29%2F%28x%28x-30%29%29 + x%2F%28x%28x-30%29%29 = 1%2F63

%28x-30%2Bx%29%2F%28x%28x-30%29%29 = 1%2F63

%282x-30%29%2F%28x%28x-30%29%29 = 1%2F63

Cross-multiply:

x%28x-30%29 = 63%282x-30%29

x%5E2+-+30x = 126x+-+1890

x%5E2+-+156x+%2B+1890= 0

Using the quadratic formula, you get two solutions:

x = 78+%2B+3sqrt%28466%29%29 = 142.76
x = 78+-+3sqrt%28466%29 = 13.24

You can eliminate the second solution, x = 13.24, because if you use that solution, Billy's rate of work, 1%2F%28x-30%29 of the lawn per minute, would be 1%2F%28-16.76%29. Since that is a negative rate of work, this is impossible.

We are left with x = 142.76. We are looking for how long it would take Bobby to mow the lawn himself. Bobby's rate of work is 1%2Fx of the lawn per minute, or 1%2F142.76 of the lawn per minute. This means it takes Bobby 142.76 minutes to mow the lawn himself.