SOLUTION: A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and empty tank can be filled in 45 minutes with the inlet pipe open

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and empty tank can be filled in 45 minutes with the inlet pipe open      Log On


   

Question 121031: A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?

Make this chart:

             Tanks filled     Rate in tanks/minute     Time in minutes 
Inlet pipe                                                      
Drain pipe                                                     
Both open        

We read
>>...A full tank can be emptied in 30 minutes if the drain is opened...<<<

If we consider filling 1 tank as positive one (+1) tank, then we must consider
draining 1 tank as "filling -1 tanks".  (That's the way we have to learn
to think sometimes in mathematics, i.e., "undoing a positive quantity" is
interpreted as "doing a negative quantity".)

So we fill in -1 tank for "tanks filled" by the drain pipe and 30 minutes
for its time. 

             Tanks filled     Rate in tanks/minute     Time in minutes 
Inlet pipe                                                       
Drain pipe       -1                                          30
Both open                                                         

We read:
>>...empty tank can be filled in 45 minutes with the inlet pipe opened...<<

So we fill in +1 tank for tanks filled by the inlet pipe and 45 minutes
for its time. 

             Tanks filled     Rate in tanks/minute     Time in minutes 
Inlet pipe        1                                          45
Drain pipe       -1                                          30
Both open                                                       

Now we read what we are to find:

>>...If both pipes are accidentally opened when the tank is full, then 
how long will it take to empty the tank?...<<

So let t be the number of minutes, and since it say "empty" the tank, we
use "negative thinking" again and put -1 for the number of "tanks filled".
So our chart is now:


             Tanks filled     Rate in tanks/minute     Time in minutes 
Inlet pipe        1                                          45
Drain pipe       -1                                          30
Both open        -1                                           t 


Now we fill in the rates by the formula

          RATE = %28TANKS_FILLED%29%2F%28TIME_IN_MINUTES%29


             Tanks filled     Rate in tanks/minute     Time in minutes 
Inlet pipe        1                 1/45                     45
Drain pipe       -1                -1/30                     30
Both open        -1                 -1/t                      t 
  
Now we form our equation by:

RATE_OF_FIRST + RATE_OF_SECOND = THEIR_COMBINED_RATE

               1%2F45 + %28-1%2F30%29 = -1%2Ft
               1%2F45 - 1%2F30 = -1%2Ft

Can you solve that? If not post again asking how.

Solution: t = 90 minutes, or 'an hour and a half'.

Edwin