SOLUTION: For a certain bathtub the hot water faucet can fill the tub in 13 minutes. The cold water faucet can fill the tub in 7 minutes. If both faucets are used together, how long will it

Algebra ->  Human-and-algebraic-language -> SOLUTION: For a certain bathtub the hot water faucet can fill the tub in 13 minutes. The cold water faucet can fill the tub in 7 minutes. If both faucets are used together, how long will it       Log On


   



Question 1140427: For a certain bathtub the hot water faucet can fill the tub in 13 minutes. The cold water faucet can fill the tub in 7 minutes. If both faucets are used together, how long will it take to fill the tub?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The filling rate for both faucets filling the tub at the same time is the sum+of their rates.
The unit should be tub per minute.
You will then want the+reciprocal+of the result to have minute per tub.

1%2F13%2B1%2F7=1%2Ft+
%287%2B13%29%2F%2813%2A7%29=1%2Ft

20%2F91=1%2Ft+
20t=91
t=91%2F20
t=4.55 minutes<---- your answer


Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

The hot faucet fills  1%2F13  of the bathtub volume per minute.


The cold faucet fills  1%2F7  of the bathtub volume per minute.


Together, they fill  1%2F13+%2B+1%2F7 = 7%2F91+%2B+13%2F91 = 20%2F91  of the bathtub volume per minute.


It means that it will take  91%2F20  minutes = 411%2F20 minutes = 4 minutes and 33 seconds 

    to fill the bathtub if the two faucets are used together.  ANSWER

Solved.

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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.