Working together, 7 identical pumps can empty a pool in 6 hours. How many hours will it take 4 pumps to empty the same pool?
Emptying Pool with Identical Pumps
If each of those 7 pumps must work for 6 hours to empty the pool, we can conclude that it takes 42 "pump hours" to empty the pool.
6 = 42 "pump hours" to empty the pool
In other words, if there were only 1 pump, then that pump would have to work for 42 hours to empty the pool. Or, if there were 42 pumps working together, it would take them only 1 hour to empty the pool.
For this question, we need to consider 4 pumps working together. So those 42 pump hours would be distributed evenly among those 4 pumps. So
would tell us how many hours each of those 4 pumps must work.
So each pump must work for
hours and the answer is E.
Frequently Asked Questions
FAQ: Why can't I use ratios?
A: There's a crucial distinction between rates and ratios, and the information given in this question is in terms of rates: 7 pumps in/per 6 hours, not something like 7 males to 6 females in a class.
If you attempt to solve it by using ratios, you'll get an answer of x = 3.42857.... If you take a quick step back and look at this logically (which you should do for all problems once you've arrived at an answer!), that means it took 7 pumps 6 hours to empty the pool, but 4 pumps about 3 hours. How would it be possible for 4 pumps to empty the same pool in LESS time than it takes 7 pumps? That seems pretty illogical, right? Also, it's not listed as an answer choice, so that's another sign that you should try a different method.
FAQ: Why can't I just add the hours?
A: When the question asks for hours, it's asking for ordinary clock time, not "machine hours" counted separately for each device. If I start the four pumps at 9 am, then at 7:30 pm they will have emptied the pool. The question is simply how much clock time has passed from 9 am to 7:30 pm? 10.5 hr. We don't care how many different devices were running during that time, how many kilowatt-hours of energy were consumed, anything like that. We literally want the clock time; how much clock time does it take, running the four pumps, to empty the pool.
FAQ: How did we get 42 "pump hours"?
A: Let's think about it this way. Instead of pumps we have workers, and you're the boss. You have a team of 7 workers and it takes them 6 hours working together to empty a pool. When you go to pay them, how many hours of work are you going to pay? If you give only 6 hours pay to split between all 7 of them, they probably won't be very happy. You'll need to pay EACH worker for the 6 hours of labor, giving a total 42 "work hours" to be paid. Each one of the 7 workers put in 6 hours of labor. That means we had 7 workers times 6 hours each, or 42 hours of labor total.
You can think of the pumps in the same way. Each one of those pumps is working for 6 hours, so we need to total the number of "work hours", and not just the overall time it took.
All the pumps empty the pool at the same rate. Whether you have 7 pumps or 4 pumps, each individual pump pumps out the same amount of water in a given amount of time. If you know that 7 pumps operating for 6 hours is how long it takes to empty an entire pool, you then know that it takes 42 total hours of "pump work" to empty the pool. You can then apply those 42 "pump hours" to 4 pumps instead of the original 7 pumps. All else equal, the 4 pumps will simply need to work the equivalent of 42 hours to empty the pool.
Watch the lessons below for more detailed explanations of the concepts tested in this question. And don't worry, you'll be able to return to this answer from the lesson page.