SOLUTION: Twin brothers Billy and bobby, can mow their grandparents lawn together in 108 minutes. Billy could now mow the lawn by himself in 35 minutes less time that it would bobby. How lon

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Question 468235: Twin brothers Billy and bobby, can mow their grandparents lawn together in 108 minutes. Billy could now mow the lawn by himself in 35 minutes less time that it would bobby. How long would it take bobby to mow the lawn by himself?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Billy and bobby, can mow their grandparents lawn together in 108 minutes.
Billy could now mow the lawn by himself in 35 minutes less time that it would bobby.
How long would it take bobby to mow the lawn by himself?
:
Let t = time for Bob to mow by himself
then
(t-35) = time for Bill to do it by himself
:
Let the completed job = 1 (a mowed lawn)
:
A typical shared work equation
:
108%2Ft + 108%2F%28%28t-35%29%29 = 1
Multiply by t(t-35), results:
108(t-35) + 108t = t(t-35)
:
108t - 3780 + 108t = t^2 - 35t
216t - 3780 = t^2 - 35t
Arrange as a quadratic equation
0 = t^2 - 35t - 216t + 3780
t^2 - 251t + 3780 = 0
Use the quadratic formula to find t
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation x=t, a=1, b= -251, c= 3780
t+=+%28-%28-251%29+%2B-+sqrt%28-251%5E2-4%2A1%2A3780+%29%29%2F%282%2A1%29+
:
t+=+%28251+%2B-+sqrt%2863001-15120+%29%29%2F2+
:
t+=+%28251+%2B-+sqrt%2847881+%29%29%2F2+
Two solutions
t+=+%28251+%2B+218.8%29%2F2+
t = 469.8%2F2
t = 234.9
and
t+=+%28251+-+218.8%29%2F2+
t = 32.2%2F2
t = 16.1
:
Only the first solution will make sense, t ~ 235 min, Bob by himself
:
:
Check this (200 min for Bill)
108%2F235 + 108%2F200 =
.46 + .54 = 1

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