SOLUTION: The Doe family is ready to fill their new swimming pool. It can be filled in 12 hours if they use their own water hose, and in 30 hours if they use Mr. Jones', their neighbor's wat

Algebra ->  Rate-of-work-word-problems -> SOLUTION: The Doe family is ready to fill their new swimming pool. It can be filled in 12 hours if they use their own water hose, and in 30 hours if they use Mr. Jones', their neighbor's wat      Log On


   

Question 1181100: The Doe family is ready to fill their new swimming pool. It can be filled in 12 hours if they use their own water hose, and in 30 hours if they use Mr. Jones', their neighbor's water hose. How long will the Doe's take to fill their pool if the neighbor's hose is used along with their own?
4 2/7 hours
6 1/2 hours
8 4/7 hours
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
The Doe family is ready to fill their new swimming pool. It can be filled in 12 hours if they use
their own water hose, and in 30 hours if they use Mr. Jones', their neighbor's water hose.
How long will the Doe's take to fill their pool if the neighbor's hose is used along with their own?
~~~~~~~~~~~~~~~~~ 

The combined rate of filling is  1%2F12+%2B+1%2F30 = 5%2F60+%2B+2%2F60  = 7%2F60  of the pool volume per hour.


It means that two hoses will fill the pool in  60%2F7 = 8 4%2F7 hours.

Solved, answered and explained.

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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 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(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Here is an alternative method for solving this kind of problem that many students like, because it avoids working with fractions.

Consider the least common multiple of the two times given. LCM(12,30)=60.

In 60 hours, the Doe hose could fill the pool 60/12=5 times; the Jones hose could fill the pool 60/30=2 times.

So in 60 hours together the two hoses could fill the pool 5+2=7 times.

That means together they can fill the one pool in 60/7 = 8 4/7 hours.

ANSWER: 8 4/7 hours