SOLUTION: My parents have to paint their house. If my son painted it alone it would take him 4 hours longer than I would take. However, if he worked with me, he would work twice as fast.

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Question 239722: My parents have to paint their house. If my son painted it alone it would take him 4 hours longer than I would take. However, if he worked with me, he would work twice as fast. Develop a formula for how long it would take both of us working together. Simplify/reduce to lowest terms.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
If my son painted it alone it would take him 4 hours longer than I would take. However, if he worked with me, he would work twice as fast. Develop a formula for how long it would take both of us working together. Simplify/reduce to lowest terms.
:
Let x = time required by you working alone
then
(x+4) = time required by son working alone
.5(x+4) = time if he worked twice as fast
:
Let y = time working together
:
Let the completed job = 1
:
+ = 1
:
multiply both sides .5x(x+4)
.5(x+4)y + xy = .5x(x+4)
Factor out y
y(.5(x+4) + x) = .5x(x+4)
:
y(.5x + 2 + x) = .5x^2 + 2x
:
y(1.5x + 2) = .5x^2 + 2x
:
y =
Where
y = hrs when working together using Dad's time working alone (x)
;
:
Prove that, assume dad can do it in 12 hrs, x = 12, find y
y =
y =
y =
y = 96/20
y = 4.8 hrs working together
:
:
Check this in the shared work equation (son's time .5(12+4) = 8 hrs
+
.4 + .6 = 1; the completed job!
:
Interesting that the son does more work than the dad except when dad does the job in 4 hrs, then they share the work equally, and do it in two hours
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An interesting problem, thanks for submitting it.