Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes eighteen hours using...?

Question

Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes eighteen hours using both hoses. They also know that Bob's hose, used alone, can fill the pool in six hours less than Jim's hose. How much time is required by each hose alone?

Answer 1

If Jim's hose fills the pool in x hours, that means it fills the fraction 1/x of the pool in each hour. Since Bob's hose takes six hours less than that, Bob's hose fills 1/(x-6) of the pool each hour. So working together, the two hoses fill the fraction (1/x) + [1/(x-6)] of the pool each hour. However we already know that working together they fill 1/18 of the pool in an hour; therefore we have the equation (1/x) + [1/(x-6)] = 1/18. That winds up being a quadratic with two solutions: about 39.248 and about 2.752. But that second solution wouldn't make sense because x - 6 would be negative. So Jim's hose takes about 39.248 hours, and Bob's takes about 33.248.

Answer 2

Bob's hose takes b hours to fill the pool, and fills 1/b of the pool per hour

Jim's hose takes 6 hours more, or b + 6, and fills 1 / (b + 6) of the pool per hour



together, they take 18 hours, and fill 1 /18 of the pool per hour



combine: 1/b + 1/(b + 6) = 1/18



multiply by 18b(b +6) to clear the fractions:

18(b +6) + 18b = b(b + 6)

18b + 108 + 18b = b^2 + 6b

0 = b^2 - 30b - 108

using the quadratic formula, b = 33.25 (discarding the negative root for time)

b + 6 = 39.25



check: 1 / 33.25 + 1 / 39.25 = 1/18 works



so Bob's hose can fill the pool is 33.25 hours, and Jim's hose can do it in 39.25 hours

Answer 3

Bob's hose takes 8 hours and Jim's hose takes 12 hours

Answer 4

Let Bob takes A hours to fill up the pool

so in 1 hour, 1/A th of the pool filled up

Let Jim takes B hours to fill up the pool.

so in 1 hour, 1/B th of the pool filled up

Also given A = B-6

SO, in i hour total of (1/b+1/j) pool is filled up

(1/(B-6) + 1/B) = (B + (B-6)) / B(B-6) = (2B-6) / B(B-6)

also given it takes 18 hours to fill up the pool when working

so, which means only 1/18 of the pool is filled up in 1 hour, hence

(2B-6) / B(B-6) = 1/18

(B-21)^2 = 333

B-21 = 18.25 or

B = 39.25 hrs

now, since A = B-6 = 39.25-6

A= 33.25hrs