SOLUTION: Working together, a man and his two sons assembled a set of electric trains in 12 minutes. Working alone, it would have taken the man 10 minutes less than it would have taken eithe

Question 612322: Working together, a man and his two sons assembled a set of electric trains in 12 minutes. Working alone, it would have taken the man 10 minutes less than it would have taken either son working alone. How long would it have taken the two sons, working together without their father, to assemble the set of trains?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Working together, a man and his two sons assembled a set of electric trains in 12 minutes.
Working alone, it would have taken the man 10 minutes less than it would have taken either son working alone.
How long would it have taken the two sons, working together without their father, to assemble the set of trains?
:
let s = time required by one of the two sons alone
then
(s-10) = time required by the father alone
:
let the completed job = 1; (assembled trains)
:
All working
+ + = 1
Add like terms
+ = 1
multiply by s(s-10),results
24(s-10) + 12s = s(s-10)
24s - 240 + 12s = s^2 - 10s
36s - 240 = s^2 - 10s
Combine into a quadratic equation on the right
0 = s^2 - 10s - 36s + 240
s^2 - 46s + 240 = 0
Factors to
(s-6)(s-40) = 0
s = 40 min is the only reasonable answer, one son working alone
:
"How long would it have taken the two sons, working together without their father, to assemble the set of trains?"
:
Two should be able to do it in half the time of one: 20 min

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