SOLUTION: Twin brothers, person A and person B, can mow their grandparents lawn together in 42 minutes. Person B takes 13 minutes more than person A. How long does it take each person to m

Question 628073: Twin brothers, person A and person B, can mow their grandparents lawn together in 42 minutes. Person B takes 13 minutes more than person A. How long does it take each person to mow alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Twin brothers, person A and person B, can mow their grandparents lawn together in 42 minutes.
Person B takes 13 minutes more than person A.
How long does it take each person to mow alone?
:
let t = time required by A to mow it alone
then
(t+13) = time required by B
Let the completed job = 1 (a mowed lawn)
:
A shared work equation
:
+ = 1
multiply by x(x+13), resulting in eliminating the denominators,
42(x+13) + 42x = x(x+13)
:
42x + 546 + 42x = x^2 + 13x
84x + 546 = x^2 + 13x
0 = x^2 + 13x - 84x - 546
A quadratic equation
x^2 - 71x - 546 = 0
You can use the quadratic formula here, but this will factor
(x+7)(x-78) = 0
the positive solution
x = 78 minutes, A alone
then
78+13 = 91 min. B alone
:
:
See if that works out
on a calc:
42/78 + 42/91 = 1
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