SOLUTION: Pipe A takes 16 min to fill a tank. Pipes B and C, whose cross-sectional circumferences are in the ratio 2:3, fill another tank twice as big as the first. If A has a cross-sectiona

Algebra.Com
Question 824377: Pipe A takes 16 min to fill a tank. Pipes B and C, whose cross-sectional circumferences are in the ratio 2:3, fill another tank twice as big as the first. If A has a cross-sectional circumference that is one-third of C, how long will it take for B and C to fill the second tank? (Assume the rate at which water flows through a unit cross-sectional area is same for all the three pipes.)
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
Pipe A takes 16 min to fill a tank.
So pipe A's filling rate is 1 tank per 16 min or  or 
A has a cross-sectional circumference that is one-third of C
Therefore C's cross-sectional circumference is 3 times A's cross-sectional
circumference, and since area varies as the square of the circumference,
C's cross-sectional area is 3² or 9 times A's cross-sectional area. 

Since
the rate at which water flows through a unit cross-sectional area is same for all the three pipes
 therefore:

Pipe C's filling rate is 9 times A's filling rate or 
Pipes B and C's cross-sectional circumferences (are) in the ratio 2:3
Since area varies as the square of the circumference. their cross-sectional
areas are in the ratio of 2²:3² or 4:9, and since the rate at which water flows
through a unit cross-sectional area is same for all the three pipes, pipe B's
filling rate is ths of C's filling rate or  or .

Pipes B and C fill another tank twice as big as the first.
how long will it take for B and C to fill the second tank?
B's and C's combined filling rate is 

+ = + =  
 
Since the second tank is twice as big as the first tank (I assume in volume),
it is the same as if they filled 2 tanks the size of the tank that A fills.

We will borrow the equation (rate)(time)=(distance covered), from motion
problems, by replacing "distance covered" by "tanks filled". 

Let t = the number of minutes it will take B and C to fill 2 tanks:

Then (B and C's combined rate)(time) = (2 tanks) 


       t = 2

Multiply both sides by 
    
          t = 2·
          t =  = 2.461538462 or about 2.5 minutes.

Edwin

RELATED QUESTIONS

2) Pipe A can fill a tank in 4hr. Pipe B can fill the tank in 9hr less than the time it... (answered by ankor@dixie-net.com)
Pipe A takes 20min to fill tank while pipe B Takes 30 min and pipe C Takes 40 min to... (answered by Seutip)
Pipe A can fill a tank in 4 h. Pipe B can fill the tank in 9 h less than the time it... (answered by josmiceli)
one pipe can fill a tank in 2 hours and another in 3 hours. how long will it take to fill (answered by josgarithmetic)
Pipe A can fill a tank in 6 hours, and pipe B can fill it in 2 hours less time than it... (answered by richwmiller,Edwin McCravy,AnlytcPhil)
A certain pipe can fill up a tank 2 hours faster than another pipe. It takes 3 hours for... (answered by josgarithmetic)
Pipe A can fill a tank in 4h. Pipe B can fill the tank in 9 h less than the time it takes (answered by jrfrunner)
A small pipe can fill a tank in 8 min more time than it takes a larger pipe to fill the... (answered by ikleyn)
Pipe A can fill a tank in 5 hours. Pipe B can fill the tank in 2 hours less time than it... (answered by stanbon,ankor@dixie-net.com)