SOLUTION: Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool tog

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool tog      Log On


   

Question 110851: Jim can fill a pool carrying bucks of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jim can fill a pool carrying buckets of water in 30 minutes. Sue
can do the same job in 45 minutes. Tony can do the same job in
1 ½ hours. How quickly can all three fill the pool together?
:
Let t = time required if they work together
:
Let 1 = the full pool
:
Convert 1.5 hrs to minutes: 90 min
:
A simple equation:
t%2F30 + t%2F45 + t%2F90 = 1
:
Multiply equation by 90, this get rid of the denominators;
You then have
3t + 2t + t = 90
:
6t = 90
t = 90/6
t = 15 minutes working together:
:
Check solution:
15/30 + 15/45 + 15/90 =
1/2 + 1/3 + 1/6 =
3/6 + 2/6 + 1/6 = 1