Question 30487
Hello!
There's a mistake in your solution. You know that it takes 18 hours using both hoses at the same time, but this is more time than what you found for each hose separately. If 2 hoses at the same time filled the pool in 18 hours, then each of them on their own should take MORE than 18 hours instead of 8 or 10. Here's how to solve this.

Let's call X to the number of hours it takes for the "slow" hose to fill the pool on its own. Therefore, the "fast" hose takes 0.8X hours to fill the pool on its own. Notice that this implies the following:

- The slow hose fills a fraction 1/X of the pool per hour (for example, if it takes 10 hours to fill the pool, it fills 1/10 of the pool per hour)

- The fast hose filles a fraction 1/(0.8X) of the pool per hour.

- Therefore, the two hoses at the same time fill a fraction {{{1/X+1/(0.8X)}}} of the pool per hour. But we also know that it takes 18 hours for both to fill the pool. So we have the equation:

{{{1/X+1/(0.8X) = 1/18}}} (since it takes 18 hours, they fill 1/18 per hour)

And now it's just a matter of isolating X from this equation:

{{{(1/X)(1+1/0.8) = 1/18}}}
{{{(1/X)2.25 = 1/18}}}
{{{(1/X)2.25 = 1/18}}}
{{{18*2.25 = X}}}
{{{X = 40.5}}}

So the slow hose takes 40.5 hours on its own to fill the pool. The fast hose takes 0.8*40.5 = 32.4 hours.

I hope this helps!

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