SOLUTION: There are three small holes in a tub filled with water. If opened, hole one will empty the tub in 3 hours; hole 2 will empty the tub in 4 hours and hole 3 will empty the tub in 5

Algebra ->  Rate-of-work-word-problems -> SOLUTION: There are three small holes in a tub filled with water. If opened, hole one will empty the tub in 3 hours; hole 2 will empty the tub in 4 hours and hole 3 will empty the tub in 5       Log On


   

Question 1091142: There are three small holes in a tub filled with water. If opened, hole one will empty the tub in 3 hours; hole 2 will empty the tub in 4 hours and hole 3 will empty the tub in 5 hours. If all 3 holes are opened at the same time, how long will it take to empty the tub?
Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
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The rate of the hole/drain 1 of emptying the tank is 1%2F3 of the tank volume per hour.

The rate of the hole/drain 2 is 1%2F4 of the tank volume per hour.

The rate of the hole/drain 3 is 1%2F5 of the tank volume per hour.


When all 3 holes are opened (all three drains are turned ON), their combined rate is 1%2F3+%2B+1%2F4+%2B+1%2F5 = 20%2F60+%2B+15%2F60+%2B+12%2F60 = 47%2F60 of the tank volume per hour.


Hence, it will take  60%2F47 hours = 1 13%2F47 hours to empty the tank if all three holes are opened.

Solved.


It is a 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".