SOLUTION: A regular tank can be filled with water by two pipes (one larger, one smaller) in 11 1/9 mins. If the larger pipe alone takes 5 mins less to fill the tank than the smaller pipe, fi

Algebra ->  Inverses -> SOLUTION: A regular tank can be filled with water by two pipes (one larger, one smaller) in 11 1/9 mins. If the larger pipe alone takes 5 mins less to fill the tank than the smaller pipe, fi      Log On


   

Question 77794: A regular tank can be filled with water by two pipes (one larger, one smaller) in 11 1/9 mins. If the larger pipe alone takes 5 mins less to fill the tank than the smaller pipe, find the time each pipe takes to fill the tank?
p/s: I know the answer can be evaluated uses this equation,
1/x + 1/(x-5) = 1/(11 1/9)
x (smaller tank) = Ans, x-5 (larger tank) = Ans
where x is the amount of time required for the smaller tank alone to fill the tank.
BUT,
1)WHY do you use the reciprocal of each to derive at the equation?
2)What is the concept behind the equation here? Has it got to do with the definition of reciprocals? or do we solve it using ratio?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
RATE--- IS THE CONCEPT BEHIND THE EQUATION
Example:
Pipe 1 alone fills a tank in 10 min
Pipe 2 alone fills the tank in 20 min
If both are turned on together, how long will it take to fill the tank???
Pipe 1 fills at the RATE of 1/10th tank per min
Pipe 2 fills at the RATE of 1/20th tank per min
Pipe 1 + Pipe 2 fills at the rate of 1/10+1/20 or 3/20th tank per min
Let x= time to fill the tank
(3/20)(x)=1 Where 1 denotes a full tank (Multiply both sides by 20)
3x=20
x=6 2/3 min----------both working together


NOW YOUR PROBLEM
Let x= amount of time for smaller pipe to fill the tank
Then (x-5)=amount of time for larger pipe to fill the tank
NOW HERE'S WHERE THE RECIPROCAL COMES IN:
The smaller pipe fills the tank at the RATE of 1/x cu units per min
The larger tank fills the tank at the RATE of 1/(x-5) cu units per min
Together, they fill the tank at the rate of 1/x+(1/(x-5)) cu units per min
But now we are told that together the fill the tank in 11 1/9 minutes. so our equation to solve is:
(1/x+(1/(x-5))(11 1/9)=1 where 1 denotes a full tank. In fact, in each of the above reciprocals, the 1 denotes a full tank.
So, dividing both sides by 11 1/9, we get:
1/x+(1/(x-5)=1/(11 1/9)-------------- which is your equation
I assume that you have no problems solviing this eq.
Hope this helps----ptaylor