SOLUTION: Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 102 minutes. Billy could mow the lawn by himself in 20 minutes less time that it would take bobby. How
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Question 563341: Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 102 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 law by himself?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 102 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 law by himself?
:
Let b = Bobby's time by himself
then
(b-20) = Billy's time by himself
:
Let the completed job = 1 (a mowed lawn)
:
+ = 1
Multiply by b(b-20)
b(b-20)* + b(b-20)* = b(b-20)
Cancel the denominators and you have:
102b + 102(b-20) = b^2 - 20b
102b + 102b - 2040 = b^2 - 20b
204b - 2040 = b^2 - 20b
combine as quadratic equation on the right
0 = b^2 - 20b - 204b + 2040
b^2 - 224b + 2040 = 0
Use the quadratic formula to find b
In this problem; a=1; b=-224; c=2040
:
:
Two solutions, but only this one will make sense
b =
b = 214.5 minutes for Bobby to do the job alone
:
:
Check this (Billy's time 214.5 - 20 = 194.5)
+ =
.524 + .476 = 1; confirms our solution of b - 214.5 min
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