If a pipe can fill a tank in 24 hours and another pipe can empty it in 30 hours,
Practice Questions
Q1
If a pipe can fill a tank in 24 hours and another pipe can empty it in 30 hours, how long will it take to fill the tank if both pipes are opened together?
120 hours
60 hours
80 hours
40 hours
Questions & Step-by-Step Solutions
If a pipe can fill a tank in 24 hours and another pipe can empty it in 30 hours, how long will it take to fill the tank if both pipes are opened together?
Correct Answer: 120 hours
Step 1: Determine the rate at which the first pipe fills the tank. It can fill the tank in 24 hours, so its rate is 1 tank per 24 hours, or 1/24 of the tank per hour.
Step 2: Determine the rate at which the second pipe empties the tank. It can empty the tank in 30 hours, so its rate is 1 tank per 30 hours, or 1/30 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: (1/24) - (1/30).
Step 4: To subtract these fractions, find a common denominator. The least common multiple of 24 and 30 is 120.
Step 5: Convert the rates to have the common denominator of 120: (1/24) = 5/120 and (1/30) = 4/120.
Step 6: Now subtract the two rates: (5/120) - (4/120) = 1/120.
Step 7: The net rate of filling the tank is 1/120 of the tank per hour. This means it takes 120 hours to fill the tank when both pipes are open.
Rate of Work – Understanding how to calculate the rate at which pipes fill or empty a tank and how to combine these rates.
Combined Work Rate – Calculating the net effect of multiple processes working together, in this case, filling and emptying a tank.
