SOLUTION: A and B can finish the job in 6 days. A can work 5 days less than B. Find the number of days it would take each working alone to finish the job.

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Question 644417: A and B can finish the job in 6 days. A can work 5 days less than B. Find the number of days it would take each working alone to finish the job.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A and B can finish the job in 6 days.
A can work 5 days less than B.
Find the number of days it would take each working alone to finish the job.
:
Let a = time required by a working alone
then
(a+5) = time required by b working alone
Let the completed job = 1
:
6%2Fa + 6%2F%28%28a%2B5%29%29 = 1
multiply by a(a+5)
a(a+5)*6%2Fa + a(a+5)*6%2F%28%28a%2B5%29%29 = a(a+5)
cancel out the denominators
6(a+5) + 6a = a(a+5)
6a + 30 + 6a = a^2 + 5a
combine on the right
0 = a^2 + 5a - 12a - 30
A quadratic equation
a^2 - 7a - 30 = 0
Factors to
(a-10)(a+3) = 0
The positive solution is all we want here
a = 10 hrs A's time working alone
then, obviously
B requires 15 hrs working alone