SOLUTION: two pumps can fill a water tank in 216 minutes when working together. Alone, the second pump takes 6 times as long as the first to fill the tank. How many minutes would it take the

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Question 1145369: two pumps can fill a water tank in 216 minutes when working together. Alone, the second pump takes 6 times as long as the first to fill the tank. How many minutes would it take the first pump to fill the tank?
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
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            1.  ALGEBRA  solution


Let x be the rate of work  of the first tank, in "job per minute", which is "the tank volume per minute".


Then the rate of work of the second tank is    "the tank volume per minute".


In one minute, two pumps fill    of the tank volume.


It means that


    x +  = .


Multiply both sides of this equation by 216.  You will get


    216x + 36x = 1,

    252x = 1

    x    = .


Hence, the first pump will fill the tank in 252 minutes, working alone.    ANSWER


            2.  Mental solution  (logical reasoning)


The first, faster pump works as productively, as 6 slower pumps.


So, the given info, if reformulated, says that 6+1 = 7 slower pumps will fill the tank in 216 minutes.


Hence, one slower pump will do it in 7*216 minutes.


The faster tank will do it 6 times faster, i.e. in   = 7*36 = 252 minutes.


You got the same answer as above.

My congrats (!)

Now you know TWO METHODS to solve the problem.

------------------

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 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.



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