SOLUTION: One pump can fill a gas tank in 8 hours. With a second pump working simultaneously, the tank can be filled in 3 hours. How long would it take the second pump to fill the tank oper

Algebra ->  Rate-of-work-word-problems -> SOLUTION: One pump can fill a gas tank in 8 hours. With a second pump working simultaneously, the tank can be filled in 3 hours. How long would it take the second pump to fill the tank oper      Log On


   

Question 1196928: One pump can fill a gas tank in 8 hours. With a second pump working simultaneously, the tank can be filled in 3 hours. How long would it take the second pump to fill the tank operating alone?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
One pump can fill a gas tank in 8 hours.
With a second pump working simultaneously, the tank can be filled in 3 hours.
How long would it take the second pump to fill the tank operating alone?
~~~~~~~~~~~~~~~~~~ 

As the problem says, the combined rate of work of two pumps is  1%2F3  of the tank volume per hour.

The rate of work of one pump is  1%2F8  of the tank volume per hour.


Hence, rate of work of the second pump is the difference

    1%2F3 - 1%2F8 = 8%2F24 - 3%2F24 = 5%2F24 of the tank volume per hour.


It means that the second pump will fill the tank in  

    24%2F5 = 44%2F5 hours,  or 4 hours and 48 minutes.    ANSWER

Solved.

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

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.




Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor shows a typical formal algebraic solution.

Here are a couple of less formal methods for solving this kind of problem, if formal algebra is not required.

(Note, however, that even if a formal algebraic solution is required, you can get good mental exercise (and good problem-solving experience) by solving the problem using logical reasoning.)

One common alternative to the solution method shown by the other tutor is to consider the least common multiple of the two given times, which is 24 hours.

In 24 hours the one pump could fill the tank 24/8 = 3 times; in 24 hours the two pumps together could fill the tank 24/3 = 8 times.

That means the other pump could fill the tank 8-3 = 5 times in 24 hours; and that means it could fill the one tank in 24/5 hours, or 4 4/5 hours, or 4 hours 48 minutes.

And another solution method using logical reasoning is that, because the one pump can fill the tank alone in 8 hours and the two pumps together can fill it in 3 hours, in those 3 hours the one pump can fill 3/8 of the tank.

That means in those 3 hours the other pump can fill 5/8 of the tank; and that means the number of hours required for the other pump alone to fill the tank is 3(8/5) = 24/5 hours.