Question 1197406
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5 & 1/2 hours = 5.5 hours

 
Let's say the task is to pump out 550 gallons of water in total.
I chose this number since it's a multiple of 5.5; but feel free to pick something else and the final answer will still be the same.


Two pumps work at the same rate, so we split the job into two equal parts. 
Pump A drains 550/2 = 275 gallons and pump B gets the other 275 gallons.


If pump A needs 5.5 hours to drain 275 gallons, then the unit rate is
275/5.5 = 50 gallons per hour
After each hour, pump A is able to drain 50 gallons of water.
Pump B has the same unit rate as pump A.


If we have 3 pumps working at this same rate, then the combined unit rate is 3*50 = 150.
After each hour, the three pumps collectively drain 150 gallons of water.
This assumes neither pump hinders one another.


Then we can say this:
time = (amount done)/(unit rate)
time = (550 gallons)/(150 gallons per hour)
time = 11/3 hours


It will take the three pumps 11/3 hours to get the job done if they work together, and neither pump hinders one another.


Then let's convert to a mixed number
11/3 = (9+2)/3
11/3 = 9/3+2/3
11/3 = 3+2/3


This means
11/3 hours = 3 hours + 2/3 of an additional hour


1 hour = 60 min
(2/3)*(1 hour) = (2/3)*(60 min)
2/3 hour = 40 min


So 3 hours + 2/3 hour = <font color=red>3 hours + 40 minutes is the final answer</font>


In terms of purely minutes only, we can say
3 hours + 40 min = 3*60 min + 40 min
3 hours + 40 min = 180 min + 40 min
3 hours + 40 min = 220 min


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Here's an algebraic approach:


x = total number of gallons to drain


If two pumps work together at the same rate, then each pump drains x/2 = 0.5x gallons of water


If the two pumps take 5.5 hours each, then,
unit rate = (amount done)/(time)
unit rate = (0.5x gallons)/(5.5 hours)
unit rate = 0.5x/5.5 gallons per hour
unit rate = 5x/55 gallons per hour
unit rate = x/11 gallons per hour
This is the unit rate for each identical pump.


Triple this unit rate to now include the third pump helping out
3*(x/11) = 3x/11
This represents the combined unit rate.


Then,
time = (amount done)/(unit rate)
time = (x gallons)/( 3x/11 gallons per hour )
time = x*(11/(3x)) hours
time = 11/3 hours
That then converts to <font color=red>3 hours + 40 minutes</font> as shown above.


The algebraic approach is useful to see that there wasn't anything special with 550 I picked earlier. 
But for some students, the numeric approach in the first section is easier to grasp. 
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