SOLUTION: A tank can be filled by big pump in 20 hours and by a small pump in 80 hours.How long will it take to fill the tank both pumps together?

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Question 1066224: A tank can be filled by big pump in 20 hours and by a small pump in 80 hours.How long will it take to fill the tank both pumps together?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
rate * time = quantity or work produced.

rate is in fraction of the pope filled in one hour.
time is in hours.
quantity is one full pipe.

for big pump, this formula becomes rate * 80 = 1
solve for rate to get rate of big pipe = ability to fill 1/80 of the pipe per hour.

for little pump, this fornmla becomes rate * 40 = 1
solve for rate to get rate of little pipe = ability to fill 1/40 of the pipe per hour.

when they work together, their rates are additive.

you get (1/40 + 1/80) * time = 1

1/40 * 2/2 = 2/80.

(2/80 + 1/80) * time = 1 becomes 3/80 * time = 1

solve for time to get time = 1/(3/80) = 1 * 80/3 = 26 and 2/3 hours.

when they work together they can fill the pipe in 26 and 2/3 hours.

to confirm:

rate of 3/80 of the pipe per hour times 80/3 hours = 1 full pipe.

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.
For many other similar solved joint-work problems with detailed explanations 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
in this site.

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".