SOLUTION: Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 69 minutes. Billy could mow the lawn by himself in 15 minutes less time that it would take Bobby. How l

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Question 468221: Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 69 minutes. Billy could mow the lawn by himself in 15 minutes less time that it would take Bobby. How long would it take Bobby to mow the lawn by himself?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Bobby takes x hours
so he does 1/x of the job in 1 minute
Billy mows in x-15 minutes
so he does 1/(x-15)of the job in 1 minute
together they do in 69 minutes
so they do 1/69 of the job in 1 minute
1%2Fx+%2B+1%2F%28x-15%29+=+1%2F69
LCD = 69x(x-1)
Multiply the equation by the LCD
69%28x-1%29%2B+69x=+x%28x-1%29
69x-69+69x=x^2-x
x^2-x-138x=-69
x^2-139x+69=0
Find the roots of the equation by quadratic formula

a= 1 ,b= -139 ,c= 69

b^2-4ac= 19321 -276
b^2-4ac= 19045
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-12%2Bsqrt%2824%29%29%2F%2812%29
x1=( 139 + 138 )/ 2
x1= 138.5
x2=( 139 -138 ) / 2
x2= 0.5
Bobby takes 138.5 minutes
Billy takes 125.5 minutes