One pump can fill a reservoir in 60 hours. Another pump can fill the same reservoir in 80 hours. A third pump can empty the reservoir in 90 hours. If all three pumps are operating at the same time, how long will it take to fill the reservoir?
i got 55.38 hours but i want to know how many minutes are in 0.38 of an hour also i want to know if this is correct
i just remembered that it says how many hour so woul it be 55 hours or 56 becuse of the .38
I don't see where it wants the number of hours only.
I see "how long will it take ....."
your answer of 55.3846... is correct
so that would be 55 hours and .3846... of an hour
so .3846..(60) = 23.0769... minutes
if you wanted it broken down into seconds, use the decimal .0769(60) seconds or appr 4.6 seconds
in time notation:
55 : 23 : 4.6 --- hours : minutes : seconds
To find out how many minutes are in 0.38 of an hour, you can multiply 0.38 by 60, since there are 60 minutes in an hour.
0.38 * 60 = 22.8
Therefore, 0.38 of an hour is equal to 22.8 minutes.
To determine if your answer of 55.38 hours is correct, we need to calculate the combined rate at which the pumps fill the reservoir.
The first pump fills the reservoir in 60 hours, so its rate of filling is 1/60 of the reservoir per hour.
The second pump fills the reservoir in 80 hours, so its rate of filling is 1/80 of the reservoir per hour.
The third pump empties the reservoir in 90 hours, so its rate of emptying is -1/90 of the reservoir per hour (negative because it empties the reservoir).
To determine the combined rate, we sum the rates of the pumps:
1/60 + 1/80 - 1/90 = (4/240) + (3/240) - (2/180) = 5/240 - 2/180
To calculate the time it takes to fill the reservoir when all three pumps are operating, we use the formula:
time = 1 / combined rate
time = 1 / (5/240 - 2/180)
To simplify further, we can find a common denominator for the fractions:
time = 1 / (1/48 - 1/90)
To subtract the fractions, we find a common denominator of 2,160:
time = 1 / ((90 - 48) / 2,160)
= 1 / (42 / 2,160)
= 1 / 0.0194
Using a calculator, we can find:
time ≈ 51.55 hours
Therefore, it will take approximately 51.55 hours (or 51 hours and 33 minutes) to fill the reservoir when all three pumps are operating together.
So, it seems that your answer of 55.38 hours is not correct.
To find out how many minutes are in 0.38 of an hour, you can multiply 0.38 by 60, as there are 60 minutes in an hour.
0.38 * 60 = 22.8
Therefore, 0.38 of an hour is equal to 22.8 minutes.
To solve the problem of how long it will take to fill the reservoir with all three pumps operating at the same time, we need to calculate the combined rates of the pumps and use that information to find the time.
Let's start by finding the rates at which each pump individually fills or empties the reservoir:
- Pump 1 fills the reservoir in 60 hours, so its filling rate is 1/60 reservoir per hour.
- Pump 2 fills the reservoir in 80 hours, so its filling rate is 1/80 reservoir per hour.
- Pump 3 empties the reservoir in 90 hours, so its emptying rate is 1/90 reservoir per hour.
Now, let's calculate the combined rate of the three pumps working together:
Combined filling rate = Pump 1 + Pump 2 - Pump 3
= 1/60 + 1/80 - 1/90
= (4/240) + (3/240) - (2/180)
= (7/240) - (2/180)
= (7/240) - (4/360)
= (7/240) - (2/90)
= (7/240) - (16/720)
= (7/240) - (4/135)
= (7*135 - 4*240) / (240*135)
= (945 - 960) / 32,400
= -15 / 32,400
The combined filling rate is negative because of the emptying pump. This means that the combined pumps will empty the reservoir instead of filling it, and it will never be filled.
Therefore, your answer of 55.38 hours is incorrect. The reservoir cannot be filled with the given pump capacities and operating times.