SOLUTION: A large pump can fill a water tank in 8 hours, and a smaller pump can fill it in 24 hours. In order to fill an empty tank, the small pump is operated for 6 hours, and then the larg

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A large pump can fill a water tank in 8 hours, and a smaller pump can fill it in 24 hours. In order to fill an empty tank, the small pump is operated for 6 hours, and then the larg      Log On


   



Question 1080404: A large pump can fill a water tank in 8 hours, and a smaller pump can fill it in 24 hours. In order to fill an empty tank, the small pump is operated for 6 hours, and then the large pump is also turned on. In total, how many hours will be required to fill the tank this way?
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
If you know the basics, you can solve everything.
If you don't know basics, there is nothing you can do.

To learn the basics, read these lessons explaining how to solve joint-work problems
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".


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Regarding your problem:

The rate of work of the large pump is 1%2F8: it fills 1%2F8 of the tank volume per hour.

The rate of work of the small pump is 1%2F24: it fills 1%2F24 of the tank volume per hour.

Their combined rate of work is 1%2F8+%2B+1%2F24 = 3%2F24+%2B+1%2F24 = 4%2F24 = 1%2F6 of the tank volume per hour.


After operating for 6 hours, the small pump filled 6%2A%281%2F24%29 = 1%2F4 of the tank volume.

Hence, it will take %28%283%2F4%29%29%2F%28%281%2F6%29%29 = %283%2A6%29%2F4 = 18%2F4 = 9%2F2 hours = 4 hours and 30 minutes for two pump to fill 
the remaining 3%2F4 of the tank volume working together.

Solved.