If pump A and pump B work together, they can fill a pool in 4 hours. Pump A, working alone, takes 6 hours to fill the pool. How long would it take pump B, working alone, to fill the pool?
rate of pump A = 1/6
rate of pump B = 1/x
combined rate = 1/6 + 1/x
= (x+6)/(6x)
time at combined rate = 1/( (x+6)/6x )
= 6x/(x+6)
but 6x/(x+6) = 4
6x = 4x+ 24
2x = 24
x = 12
Pump B alone would take 12 hours
check:
combinedrate =1/12 + 1/6 = 3/13 = 1/4
time at combined rate = 1/(1/4)) = 4
To solve this problem, we can use the concept of rates. Let's assume that pump A and pump B each have individual rates of filling the pool.
Let's say that the rate of pump A is R_A, and the rate of pump B is R_B.
We are given that when pump A and pump B work together, they can fill the pool in 4 hours. This means that their combined rate is 1/4 of the pool per hour.
From this information, we can write the following equation:
R_A + R_B = 1/4 ---(equation 1)
We are also given that pump A, working alone, takes 6 hours to fill the pool. This means that the rate of pump A is 1/6 of the pool per hour.
From this information, we can write the following equation:
R_A = 1/6 ---(equation 2)
Now, let's substitute equation 2 into equation 1 to solve for the rate of pump B:
1/6 + R_B = 1/4
R_B = 1/4 - 1/6
R_B = (3/12) - (2/12)
R_B = 1/12
This means that pump B can fill 1/12 of the pool per hour.
To find out how long it would take pump B, working alone, to fill the pool, we need to find the reciprocal of its rate:
1 / (1/12) = 12/1
Pump B, working alone, can fill the pool in 12 hours.
Therefore, it would take pump B, working alone, 12 hours to fill the pool.