SOLUTION: I have a tank that can be filled by a small pipe in 12 hours or by a large pipe in 8 hours. Suppose I start filling the tank with the large pipe for two hours. After that 2 hours i

Question 548244: I have a tank that can be filled by a small pipe in 12 hours or by a large pipe in 8 hours. Suppose I start filling the tank with the large pipe for two hours. After that 2 hours is up, I use both pipes and continue filling the tank for a length of time, t. I then turn off the large pipe and it takes 2 more hours to fill the tank with just the small pipe. How long of a time is t?
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
I have a tank that can be filled by a small pipe in 12 hours or by a large pipe in 8 hours.
Suppose I start filling the tank with the large pipe for two hours.
After that 2 hours is up, I use both pipes and continue filling the tank for a length of time, t.
I then turn off the large pipe and it takes 2 more hours to fill the tank with just the small pipe.
How long of a time is t?
:
Let the completed task = 1 (a full tank)
:
from the given information:
(t+2) = filling time of the large pipe
and
(t+2) = filling time of the smaller
:
+ = 1
Multiply by 24, results:
2(t+2) + 3(t+2) = 24
2t + 4 + 3d + 6 = 24
2t + 3t = 24 - 10
5t = 14
t =
t = 2.8 hrs
;
:
See if that checks out
+ =
+ =
.4 + .6 = 1
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
In words:
( portion of the tank filled ) = ( rate of filling ) x ( time spent filling )
Rate using small pipe: ( 1 tank ) / ( 12 hrs )
Rate using large pipe: ( 1 tank ) / (8 hrs )
----------------------------------
Using large pipe for 2 hrs:
Portion of tank filled is
There is of the tank left to be filled
----------------------------------
Using both pipes, add their rates of filling
to get rate together

Now the fraction of the tank left to be filled
is
------------------
Using the small pipe for 2 more hrs

hrs
min
is 2 hrs and 48 min
I may have made a mistake, but
I think the method is good

RELATED QUESTIONS
A water tank can be filled with a large inlet pipe and a small inlet pipe in three hours. (answered by josmiceli)
A tank can be filled by an inlet pipe in 7 hours. While a drain pipe can empty the tank... (answered by richwmiller)
A tank can be filled by an inlet pipe in 7 hours. While a drain pipe can empty the tank... (answered by Edwin McCravy)
a tank can be filled in 18 hours by pipe A or in 24 hours by pipe B.how long would it... (answered by richwmiller)
it takes 6.5 hours to fill a large tank with oil using Pipe a. using both pipe a and b,... (answered by richwmiller)
A milk tank can be filled by pip A in 6 hours, by pipe B in 8 hours and by pipe C in 12... (answered by mananth)
A water tankin a farm can be filled using both a large inlet pipe and a small inlet... (answered by josgarithmetic)
A ttank can be filled in 18. Hours by pipe a or in 24. Hours by pipe... (answered by checkley79)
A tank can be filled in 18 hours by Pipe A or 24 hours by Pipe B. How long would it take... (answered by venugopalramana)