How long does it take?

Question

It takes hose A six hours to fill a swimming pool. It takes hose B 3 hours to fill the same swimming pool. It takes hose C 2 hours to fill the swimming pool. If all three of them were filling the pool at the same time, how long would it take to fill the pool? Is it 1 hour because I subtracted 6 and 3 which equals 3 then I subtracted 3 and 2.

Answer 1

I had trouble with these problems as a youngster, mostly because nobody ever explained a logical procedure for solving them. Perhaps I can undo this wrong for you.

Lets say it takes six hours to fill a pool for hose A. That implies a rate of filling defined in funny units:

1 pool filled per 6 hours

Now, we have another rate, hose B:

1 pool filled per 3 hours

And for hose C?

1 pool filled per 2 hours.

Now, just add up the rates:

1/3 + 1/2 + 1/6 = 2/6 + 3/6 + 1/6 = 1

The combined rate for all three filling is:

1 pool filled per 1 hour.

Answer 2

Hose A is 1 pool/6 hr
Hose B is 1 pool/3 hr
Hose C is 1 pool/2 hr

Running them all the same time is:

1/6 + 1/3 + 1/2 = 1 pool/x hr Multiply all terms by 6x.
x + 2x + 3x = 6
6x = 6
x = 1 hour

Same answer, but a different reason.
So in one hour, the first hose fills 1/6 of the pool, the second hose fills 1/3 of the pool, and the third hose fills 1/2 of the pool. 1/6 + 2/6 + 3/6 = 1
x = 1/6

Answer 3

This is a rate problem.

One way to approach it would be to see how much each hose would fill within one hour.

So hose A would fill 1/6 of the pool in one hour.
Hose B would fill 1/3 of the pool in one hour.
Hose C would fill 1/2 of the pool in one hour.

Add these fractions to see how much you would fill altogether in one hour.

1/6 + 1/3 + 1/2 = 6/6

So it turns out for this problem that it only takes one hour to fill the entire pool. So your answer was right, but your method of finding the time was incorrect.

Answer 4

yh it does take one hour beause
6 hours = 1/6
3 hours = 2/6
2 hours = 3/6

so if u add them all together they equal one

Answer 5

Do your own homework

Answer 6

as long as it freakin takes.