SOLUTION: Pump A and pump B each can empty a tank in 2 hours. Another pump, C, can empty the tank using double the time of pump A. If all three pumps are working together at the same time, h

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Pump A and pump B each can empty a tank in 2 hours. Another pump, C, can empty the tank using double the time of pump A. If all three pumps are working together at the same time, h      Log On


   

Question 1116569: Pump A and pump B each can empty a tank in 2 hours. Another pump, C, can empty the tank using double the time of pump A. If all three pumps are working together at the same time, how long will it take to empty the tank?
Found 4 solutions by josgarithmetic, ikleyn, MathTherapy, greenestamps:
Answer by josgarithmetic(39613) About Me  (Show Source):
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
Since pump A can empty the tank in 2 hours, it drains  1%2F2  of the tank volume per hour.


Since pump B has the same rate of work (GIVEN !), it drains  1%2F2  of the tank volume per hour.


Since the pump C can empty the tank in 4 hours (GIVEN !), it drains  1%2F4  of the tank volume per hour.


Working together, the three pumps drain  1%2F2+%2B+1%2F2+%2B+1%2F4 = 5%2F4 of the tank volume per hour.


It means the the three pumps will empty the tank in  4%2F5 of an hour = 48 minutes working together.


Answer. It will take 48 minutes for 3 pumps to empty the tank working together.

Solved.

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It is a typical and standard joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the 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


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

Pump A and pump B each can empty a tank in 2 hours. Another pump, C, can empty the tank using double the time of pump A. If all three pumps are working together at the same time, how long will it take to empty the tank?
Pump A takes 2 hours, or can do 1%2F2 of job in 1 hour

Pump B also takes 2 hours, and also can do 1%2F2 of job in 1 hour

Pump C takes = 2(2), or 4 hours, and can do 1%2F4 of job in 1 hour

With T being time all 3 take to do the job, we get: matrix%281%2C3%2C+1%2F2+%2B+1%2F2+%2B+1%2F4%2C+%22=%22%2C+1%2FT%29

2T + 2T + T = 4 ------- Multiplying by LCD, 4T

5T = 4

T, or time taken for the 3 to do the job = 

You must know by now whose answer to IGNORE, and if possible, toss in the garbage!

Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


Being a bit less formal, you could solve the problem as described below.

Each of pumps A and B works twice as fast as pump C; that means pump A and pump B are each equivalent to two C pumps.

So A, B, and C working together is equivalent to 2+2+1 = 5 C pumps.

Since one C pump can empty the tank in 4 hours, 5 C pumps can empty the tank in 4/5 hours, or 48 minutes.