SOLUTION: Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 50 minutes for the larger hose to fill the swimming pool by itself, how l

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 50 minutes for the larger hose to fill the swimming pool by itself, how l      Log On


   

Question 614042: Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool. If it takes 50 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Working together, it takes two different sized hoses 30 minutes to fill a small swimming pool.
If it takes 50 minutes for the larger hose to fill the swimming pool by itself, how long will it take the smaller hose to fill the pool on its own?
:
Let x = time for the small hose to fill it by itself
let the completed job = 1 (a full pool)
:
Each hose will to fraction of the job, the two fractions add up to 1
30%2F50 + 30%2Fx = 1
reduce fraction
3%2F5 + 30%2Fx = 1
multiply by 5x, results:
3x + 5(30) = 5x
150 = 5x - 3x
150 = 2x
x = 150/2
x = 75 hrs, the small hose alone