SOLUTION: Could you tell me if I've presented this in the right way: Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes 18 hours usin

Question 30487: Could you tell me if I've presented this in the right way:
Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes 18 hours using both hoses. They also know that Bob's hose, used alone, takes 20% less time than Jim's hose alone. How much time is required to fill the pool by each hose alone?
let x = the faster hose
let .8x = the slower hose (80% capacity)
then
x+ .8x = 18
1.8x = 18
x = 10 hours for the faster hose
.8(10) 8 hours for the slower hose
= 18 total hours for both.
Thanks for all your help!!
Answer by mbarugel(146) (Show Source): You can put this solution on YOUR website!
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 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:
(since it takes 18 hours, they fill 1/18 per hour)
And now it's just a matter of isolating X from this equation:

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!
Get more answers at Online Math Answers.com!
RELATED QUESTIONS
Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool.... (answered by nerdybill)

Hi, I've been having trouble with this word problem and I honestly don't know where to... (answered by rfer,edjones)

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool.... (answered by scott8148)

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool.... (answered by edjones)

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool.... (answered by josmiceli)

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool.... (answered by MathTherapy)

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool.... (answered by richwmiller)

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool.... (answered by josmiceli,greenestamps)

Hi! My question is: Next-door neighbors Bob and Jim use hoses from both houses to fill (answered by rothauserc)