SOLUTION: A and B working together can do a job in 24 hours. After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours. How long would it ta

Question 149574: A and B working together can do a job in 24 hours. After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours. How long would it take each working alone to do the job?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A and B working together can do a job in 24 hours. After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours. How long would it take each working alone to do the job?
;
Let a = time required when A works alone
Let b = time required when B works alone
:
Let the completed job = 1
:
write an equation for each scenario :
"A and B working together can do a job in 24 hours."
+ = 1
Multiply equation by ab to get rid of the denominators, results
24b + 24a = ab
24a = ab - 24b
24a = b(a-24)
= b
:
"After A worked alone for 7 hours, B joined him and together they finished the rest of the job in 20 hours.
That means a worked 27 hrs
+ = 1
Multiply equation by ab to get rid of the denominators, results
27b + 20a = ab
20a = ab - 27b
20a = b(a-27)
= b
:
Therefore:
=
Cross multiply:
24a(a-27) = 20a(a-24)
:
24a^2 - 648a = 20a^2 - 480a
:
24a^2 - 20a^2 -648a + 480a = 0
:
4a^2 - 168a = 0
:
4a(a - 42) = 0
:
a = +42 A's hrs alone
;
Use + = 1 to find b, substitute 42 for a
+ = 1
Multiply equation by 42b
24b + 42(24) = 42b
:
1008 = 42b - 24b
:
1008 = 18b
b =
b = 56 hrs is B's time alone
;
:
You can check solution using a calc on both equations, a=42, b=56

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