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.

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) (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
:
+ = 1
multiply by a(a+5)
a(a+5)* + a(a+5)* = 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

RELATED QUESTIONS
A,B and C can finish a job in 6 days. If B and C work together, the job will take 9 days; (answered by stanbon,harshachittar)

A&B working together can finish painting the house in six days. A, working alone, can... (answered by ankor@dixie-net.com)

A, B and C can finish a job in 6 days. If B and C work together, the job will take 9... (answered by josmiceli)

When A,B and C work together, they can finish installing the garden in 3 days. The job... (answered by ikleyn)

A,B, and C can finish a job in 6 days. If B and C work together, the job will take 9... (answered by edjones)

a,b and c can finish a job in 6 days. if b and c work together , the job will take 9... (answered by venugopalramana)

A B and C can finish a job in 6 days. If B and C work together the job will take 9 days.... (answered by josmiceli)

A, B, and C can finish a job in 6 days. If B and C work together, the job will take 9... (answered by richwmiller)