SOLUTION: Pump A can empty a swimming pool in 5 hours, pump B can empty it in 8 hours, and pump C can empty it in 10 hours. If all three of these pumps are used together, how long will it t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Pump A can empty a swimming pool in 5 hours, pump B can empty it in 8 hours, and pump C can empty it in 10 hours. If all three of these pumps are used together, how long will it t      Log On


   

Question 1161576: Pump A can empty a swimming pool in 5 hours, pump B can empty it in 8 hours, and pump C can empty it in 10 hours. If all three of these pumps are used together, how long will it take to empty the pool?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.

Pump A makes  1%2F5  of the job per hour;

Pump B makes  1%2F8  of the job per hour;

Pump C makes  1%2F10  of the job per hour.


Working together, the three pumps make  1%2F5+%2B+1%2F8+%2B+1%2F10 = 8%2F40+%2B+5%2F40+%2B+4%2F40 = 17%2F40  of the job per hour.


Hence, it will take  40%2F17 hours = 26%2F17 hours = 2 hours and 21 minutes (approximately)  for the three pumps to empty the tank,
working tofether.

Solved.

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It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See introductory lessons
    - 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
    - Joint-work problems for 3 participants

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".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!
Here is an alternative to the traditional algebraic solution method shown by the other tutor. Many students like this alternative because it avoids working with fractions.

Consider the least common multiple of the given numbers of hours. The LCM of 5, 8, and 10 is 40.

In 40 hours, pump A could empty 40/5 = 8 pools, pump B could empty 40/8 = 5 pools, and pump C could empty 40/10 = 4 pools.

So together in 40 hours the three pumps could empty 8+5+4 = 17 pools.

So the time it takes the three of them to empty the one pool is 40/17 hours.