SOLUTION: Twin​ brothers, Billy and​ Bobby, can mow their​ grandparent's lawn together in 96 minutes. Billy could mow the lawn by himself in 20 minutes less time that it would take B

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Question 1174767: Twin​ brothers, Billy and​ Bobby, can mow their​ grandparent's lawn together in 96 minutes. Billy could mow the lawn by himself in 20 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-20%29 of the lawn per minute

Rate of work working together = 1%2Fx + 1%2F%28x-20%29 of the lawn per minute = 1%2F96 of the lawn per minute

Solve for x:

1%2Fx + 1%2F%28x-20%29 = 1%2F96

%28x-20%29%2Fx%28x-20%29 + x%2Fx%28x-20%29 = 1%2F96

%28x-20%2Bx%29%2Fx%28x-20%29 = 1%2F96

%282x-20%29%2Fx%28x-20%29 = 1%2F96

Cross-multiply:

x%28x-20%29 = 96%282x-20%29

x%5E2+-20x = 192x+-+1920

x%5E2+-20x+-+192x+%2B+1920 = 0

x%5E2+-+212x+%2B+1920 = 0

Use the quadratic formula to solve for x:

x = 106+-+2sqrt%282329%29 = 9.48
x = 106+%2B+2sqrt%282329%29 = 202.52

There are two solutions. Because Billy's rate of work is 1%2F%28x-20%29 of the lawn per minute, that means the first solution, x = 9.48, would make Billy's rate of work 1%2F%28-10.52%29. This is a negative rate and, therefore, impossible. This means we can eliminate this solution.

We are left with the solution, x = 202.52. 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. Plugging in x = 202.52, Bobby's rate of work is 1%2F202.52 of the lawn per minute. That means it would take Bobby 202.52 minutes to mow the lawn himself.