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

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) (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 and and use the following work formula:

where C equals the time it will take both A & B working together, so

substitution of known quantities

least common denominator LCD

simplification

cross multiplication

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) (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)
RELATED QUESTIONS
Tom and dick working together can perform a task in 2 hours and 24 minutes. Dick and... (answered by ikleyn)
Tom and Dick, working together, can perform a task in 2 hours and 24 minutes. Dick and... (answered by ikleyn)
one person can complete a task 8 hours sooner than another person. working together both (answered by josmiceli)
A,B and C working together can do a certain task in 6 hours. A & B can do the task in 9... (answered by ankor@dixie-net.com)
A,B and C working together can do a certain task in 6 hours. A & B can do the task in 9... (answered by ptaylor)
It takes person A 4 hours less than person B to complete a certain task. Working... (answered by josmiceli)
If two boys working together can complete a task in 2.5 hours and A working alone can... (answered by josgarithmetic)
If it takes 4 hours for one person to perform a task and it takes another person 3 hours... (answered by flame8855)
Working alone, worker A can complete a task in 3 hours; worker B can complete it in 6... (answered by eric.schuh)