SOLUTION: If A can perform a task in 24 hours and B can perform the same task in 40 hours, how long does it take A and B working together? show equation and solve

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Question 248883: If A can perform a task in 24 hours and B can perform the same task in 40 hours, how long does it take A and B working together? show equation and solve
Found 2 solutions by chosenpoint, amalm06:
Answer by chosenpoint(26) About Me  (Show Source):
You can put this solution on YOUR website!
This is a common algebraic work problem, and this following method can be used in many different ways, including solving work task problems, and problems involving filling tanks of water, etc. Lets go!

set A=24 and B=40 and use the following work formula:

1%2FA+%2B+1%2FB+=+1%2FC where C equals the time it will take both A & B working together, so

1%2F24+%2B+1%2F40=1%2FC substitution of known quantities

40%2F960+%2B+24%2F960=1%2FC least common denominator LCD

64%2F960=1%2FC simplification

64x=960 cross multiplication

C=15 solve for C and final answer

so if A and B work together, they will complete the task in 15 hours, which should make sense (ie the 2 people working together should get the task done faster than either single person can)! :)

Answer by amalm06(224) About Me  (Show Source):
You can put this solution on YOUR website!
A can finish 1/24th of the task in 1 hr
B can finish 1/40th of the task in 1 hr
Let 1 denote the full task
Then (1/24 + 1/40)(t)=1, where t denotes the time spent working together
Multiply by the LCM:
(5+3)t=120
8t=120
t=15 hr (Answer)