Two pumps of different sizes working together can empty a fuel tank is 5 hours. The larger pump can empty this tank in 4 hours less than the smaller one. If the larger one is out of order, how long will it take the smaller one to do the job alone?

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- Jun 10th 2007, 04:04 AMblueridgeTwo Pumps, One Tank
Two pumps of different sizes working together can empty a fuel tank is 5 hours. The larger pump can empty this tank in 4 hours less than the smaller one. If the larger one is out of order, how long will it take the smaller one to do the job alone?

- Jun 10th 2007, 04:10 AMQuick
I'll start you off...

Define your variables: I'd call the**b**igger pump and the**s**maller pump

the number of tanks per hour the bigger pump can empty

the number of tanks per hour the smaller pump can empty

Both of those numbers will be fractions.

Now, since you only wanted a hint, I'm only going to give you the first equation and you'll have to find the rest...

Quote:

Two pumps of different sizes working together can empty a fuel tank is 5 hours.

Do you need any more help? - Jun 10th 2007, 04:12 AMblueridgeYes
If you can set up the other equation, I can take it from there.

- Jun 10th 2007, 04:22 AMQuick
- Jun 10th 2007, 05:54 AMblueridgetell me...
I am dealing with two equations in two unknowns?

- Jun 10th 2007, 06:59 AMCaptainBlack
- Jun 10th 2007, 07:39 AMSoroban
Hello, blueridge!

Here's another approach . . .

Quote:

Two pumps of different sizes working together can empty a fuel tank is 5 hours.

The larger pump can empty this tank in 4 hours less than the smaller one.

If the larger one is out of order, how long will it take the smaller one to do the job alone?

. . In one hour, they can do of the job. .**[1]**

The smaller pump can do the job in hours. .[Note that: . .]

. . In one hour, it can do of the job.

The larger pump takes 4 hours less; it takes hours.

. . In one hour, it can do of the job.

Together, in one hour, they can do: . of the job. .**[2]**

But [1] and [2] describe the same thing:

. . the fraction of the job done in one hour.

There is our equaton! . . . .

Multiply by the common denominator:

. .

. . which simplifies to the quadratic: .

The Quadratic Formula gives us: .

Since . the solution is: .

Therefore, the smaller pump will take about 12.4 hours working alone.

- Jun 10th 2007, 11:14 AMblueridgetell me...
Soroban,

I thank you for sharing yet a more simplistic avenue to understanding this question.