SOLUTION: Machine A working alone can complete a job in 3 1/2 hours. Machine B working alone can do the same job in 4 2/3 hours. How long will it take both machines working together at their

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Machine A working alone can complete a job in 3 1/2 hours. Machine B working alone can do the same job in 4 2/3 hours. How long will it take both machines working together at their      Log On


   

Question 986933: Machine A working alone can complete a job in 3 1/2 hours. Machine B working alone can do the same job in 4 2/3 hours. How long will it take both machines working together at their respective constant rates to complete the job?
Thanks a lot for your help , very much appreciated in providing this forum
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52767) About Me  (Show Source):
You can put this solution on YOUR website!
.
Since the machine  A  working alone can complete a job in  31%2F2  hours,  it makes the part of  1:31%2F2 = 1:7%2F2 = 2%2F7  of the entire work per hour.
(It is rate of work for the machine  A).

Since the machine  B  working alone can do the same job in  42%2F3  hours,  it makes the part of  1:42%2F3 = 1:14%2F3 = 3%2F14  of the entire work per hour.
(It is rate of work for the machine  B).

Based on this data,  we can conclude that the machines  A  and  B  working together do  2%2F7 + 3%2F14 = 4%2F14 + 3%2F14 = 7%2F14 = 1%2F2  of the entire work in one hour.

Hence,  it will take  2  hours for two machines to complete the job working together.

Answer.  2 hours.

PS.  It is the standard rate-of-work problem on joint work.
You can find numerous examples of such problems in the lesson  Using fractions to solve word problems on joint work  in this site.


Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!

Machine A working alone can complete a job in 3 1/2 hours. Machine B working alone can do the same job in 4 2/3 hours. How long will it take both machines working together at their respective constant rates to complete the job?
Thanks a lot for your help , very much appreciated in providing this forum 
Time both machines take: highlight_green%282%29 hours