SOLUTION: 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 houses. They also know that Bob's hose, used alone,

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 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 houses. They also know that Bob's hose, used alone,      Log On


   

Question 23843: 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 houses. 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?
Thanks for your help!
Dan
Found 4 solutions by elima, adamhen894, josgarithmetic, ikleyn:
Answer by elima(1433) About Me  (Show Source):
You can put this solution on YOUR website!
First of all let;
x=Jim's hose
x-.20x=Bob's hose
x+(x-.20x)=18
2x-.20x=18
1.8x=18
x=10
So now we have what Jim's hose would do, and we know Bob's hose takes 20% less time, so;
10-.20=2
So bob's hose;
10-2=8
Now the two together;
10+8=18
=)

Answer by adamhen894(15) About Me  (Show Source):
You can put this solution on YOUR website!
let x be amount of time(in hours) Jim uses hose to fill the pool alone.
Bob takes 20% less time than Jim's to fill the pool alone. x-0.2x= 0.8x
it takes 18 hours for Bob and Jim to fill the pool together.
in one hour,
Jim can dnoe 1/x of job
Bob can 1/0.8x of job (also equals 5/4x)
together they can done 1/18 of job
1/x + 5/4x = 1/18
(4+5)/4x = 1/18
x=40.5 ( # of hours for Jim to fill the pool alone)
& for Bob, it takes 32.4 hour to fill the pool alone.
if you have any other ways of solving it, email me, i would love to hear that!!! adamchen894@gmail.com

Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
HOSE          FILL RATE, POOL per HOUR

BOB             1/(x-0.2x)

JIM             1/x

COMBINED        1/18


1%2F%280.8x%29%2B1%2Fx=1%2F18
-
1%2F%28%284%2F5%29x%29%2B1%2Fx=1%2F18
5%2F%284x%29%2B1%2Fx=1%2F18
5%2F%284x%29%2B4%2F%284x%29=1%2F18
9%2F%284x%29=1%2F18
9=4x%2F18
x=9%2A18%2F4=9%2A9%2F2
x=81%2F2
highlight%28x=40%261%2F2%29------------hours for Jim's hose alone to fill the pool.

highlight%2832.4%29----------------hours for Bob's hose alone

Answer by ikleyn(52759) About Me  (Show Source):
You can put this solution on YOUR website!
.
It is typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Rate of work and joint work problems" of the section "Word problems".