One pump fills a tank two times as fast as another pump. If the pumps work together they fill the tank in 18 minutes. How long does it take each pump working alone to fill the tank?
mat
P1: X min.
P2: 2x min.
2x*x/(2x+x) = 18, 2x^2/3x = 18, 2x/3 = 18, 2x = 54 min, X = 27 min.
To solve this problem, we can assign variables to the rates at which each pump fills the tank.
Let's say the slower pump fills the tank at a rate of x tanks per minute. Since the faster pump fills the tank twice as fast as the slower pump, its rate would be 2x tanks per minute.
If the two pumps work together, their combined rate is the sum of their individual rates. So the combined rate would be (x + 2x) tanks per minute, which simplifies to 3x tanks per minute.
We know that when the two pumps work together, they can fill the tank in 18 minutes. Therefore, at their combined rate of 3x tanks per minute, they fill the tank in 18 minutes. This can be expressed as the equation:
(3x) * 18 = 1
Simplifying the equation, we have:
54x = 1
To find the rate of each pump working alone, we need to solve for x. Divide both sides by 54:
x = 1/54
Now we have the rate of the slower pump, x, which is 1/54 tanks per minute.
To find the time it takes for each pump to fill the tank alone, we divide the tank's capacity by the rate of each pump.
For the slower pump, the time it takes to fill the tank alone is 1/(1/54) = 54 minutes.
For the faster pump, given that it fills the tank twice as fast as the slower pump, the time it takes to fill the tank alone is 54 / 2 = 27 minutes.
Therefore, the slower pump takes 54 minutes alone to fill the tank, while the faster pump takes 27 minutes alone to fill the tank.