Solve the problem.
-One pump can drain a pool in 4 minutes. When a second pump is also used, the pool only takes 3 minutes to drain. How long would it take the second pump to drain the pool if it were the only pump in use?
B) 11 minutes
C) 12 minutes

Question

Solve the problem.
-One pump can drain a pool in 4 minutes. When a second pump is also used, the pool only takes 3 minutes to drain. How long would it take the second pump to drain the pool if it were the only pump in use?
B) 11 minutes 
C) 12 minutes

Quizplus · Accepted Answer

Let the rate of the first pump be x and the rate of the second pump be y (in units of pool drained per minute). Then we have the equations:
x = 1/4  (because it takes one pump 4 minutes to drain the pool)
x + y = 1/3  (because it takes both pumps 3 minutes to drain the pool)
Solving for y, we get y = 1/3 - 1/4 = 1/12. So the second pump can drain the pool on its own in 12 minutes. Let's say the first pump can drain 1 unit of water in 1 minute. Therefore, the first pump can drain the entire pool consisting of x units of water in x minutes. Similarly, let's say the second pump can drain y units of water in 1 minute. Therefore, the second pump can drain the same pool consisting of x units of water in x/y minutes.

Using the given information, we can write two equations:
x/4 + x/y = 1 (Equation 1)
x/3 + x/y = 1 (Equation 2)

Subtracting Equation 1 from Equation 2, we get:
x/y = 1/3

Substituting this value in Equation 1, we get:
x/4 + 1/3*x = 1
Solving for x, we get:
x = 12

Therefore, the second pump can drain 12/y units of water in 1 minute.

Using the same method as before, we can write a new equation:
12/y = 1
Solving for y, we get:
y = 12

Hence, the second pump would take 12 minutes to drain the pool if it were the only pump in use.

Solve the Problem. -One Pump Can Drain a Pool in 4 Minutes. When