SOLUTION: One pump can fill a tank with oil in 4 hours. A second pump can fill the same tank in 3 hours. If both pumps are used at the same time, how long will they take to fill the tank?

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Question 1205982: One pump can fill a tank with oil in 4 hours. A second pump can fill the same tank in 3 hours. If both pumps are used at the same time, how long will they take to fill the tank?
I tried everything but the answer that I had wrote down from my teacher's answer is 12/7 hours
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52864)   (Show Source): You can put this solution on YOUR website!
.

Your answer is correct.


 +  =  +  = .


ANSWER.   hours.  It is 1 hours = 1 hour and 42.857 minutes.

Solved.

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Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

There are a few approaches we could take. I'll discuss two methods.

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Method 1

Let's consider a tank that is 12 gallons.
Feel free to pick any positive number you want since it turns out the capacity doesn't matter.
I'm picking 12 because it is the LCM of 3 and 4.

Pump A fills the 12 gallon tank in 4 hours when working alone.
The unit rate is 12/4 = 3 gallons per hour.
Formula: rate = (amount done)/time

Pump B fills the 12 gallon tank in 3 hours when working alone.
Unit rate = 12/3 = 4 gallons per hour.

When both pumps work together, neither pump hindering the other, their combined rate is 3+4 = 7 gallons per hour.

Then we'll use this formula
time = (amount done)/rate
to determine that 12/7 hours is the amount of time it takes when both pumps work together.

Side notes:
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Method 2

Pump A does 1 job in 4 hours when working alone.
"1 job" is defined in this case as "filling the entire tank with oil".
It's unit rate is 1/4 of a job per hour.

Pump B has a unit rate of 1/3 of a job per hour through similar logic.

Combined rate = 1/4 + 1/3 = 3/12 + 4/12 = 7/12 of a job per hour

x = number of hours to do 1 job if both pumps work together
rate*time = amount done
(7/12 of a job per hour)*(x hours) = 1 job
(7/12)x = 1
x = 12/7 hours
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