SOLUTION: Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 92 minutes. Billy could mow the lawn by himself in 25 minutes less time that is would take Bobby. How l

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Question 902254: Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 92 minutes. Billy could mow the lawn by himself in 25 minutes less time that is would take Bobby. How long would sit take Bobby to mow the lawn by himself?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx+%2B+1%2F%28x-25%29+=+1%2F92 |Multiplying thru by 92x(x-25)so as all denominators = 1
92(x-25) + 92x = x(x-25)
x^2 -209x + 2300 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-209x%2B2300+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-209%29%5E2-4%2A1%2A2300=34481.

Discriminant d=34481 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--209%2B-sqrt%28+34481+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-209%29%2Bsqrt%28+34481+%29%29%2F2%5C1+=+197.345301442776
x%5B2%5D+=+%28-%28-209%29-sqrt%28+34481+%29%29%2F2%5C1+=+11.6546985572237

Quadratic expression 1x%5E2%2B-209x%2B2300 can be factored:
1x%5E2%2B-209x%2B2300+=+1%28x-197.345301442776%29%2A%28x-11.6546985572237%29
Again, the answer is: 197.345301442776, 11.6546985572237. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-209%2Ax%2B2300+%29