If a pipe can fill a tank in 20 hours and another pipe can empty it in 25 hours, how long will it take to fill the tank if both pipes are opened together?
Practice Questions
1 question
Q1
If a pipe can fill a tank in 20 hours and another pipe can empty it in 25 hours, how long will it take to fill the tank if both pipes are opened together?
50 hours
100 hours
80 hours
40 hours
The net rate is 1/20 - 1/25 = 1/100. Therefore, it will take 100 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: If a pipe can fill a tank in 20 hours and another pipe can empty it in 25 hours, how long will it take to fill the tank if both pipes are opened together?
Solution: The net rate is 1/20 - 1/25 = 1/100. Therefore, it will take 100 hours to fill the tank.
Steps: 8
Step 1: Determine the rate at which the first pipe fills the tank. It fills the tank in 20 hours, so its rate is 1 tank per 20 hours, or 1/20 of the tank per hour.
Step 2: Determine the rate at which the second pipe empties the tank. It empties the tank in 25 hours, so its rate is 1 tank per 25 hours, or 1/25 of the tank per hour.
Step 3: Calculate the net rate when both pipes are opened together. This is done by subtracting the emptying rate from the filling rate: (1/20) - (1/25).
Step 4: To subtract these fractions, find a common denominator. The least common multiple of 20 and 25 is 100.
Step 5: Convert the rates to have the common denominator: (1/20) = (5/100) and (1/25) = (4/100).
Step 6: Now subtract the two rates: (5/100) - (4/100) = (1/100).
Step 7: The net rate of filling the tank is 1/100 of the tank per hour.
Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of the net rate: 1 / (1/100) = 100 hours.
