If a tank can be filled by a pipe in 8 hours and emptied by another pipe in 12 h
Practice Questions
Q1
If a tank can be filled by a pipe in 8 hours and emptied by another pipe in 12 hours, how long will it take to fill the tank if both pipes are opened together?
4 hours
6 hours
8 hours
10 hours
Questions & Step-by-Step Solutions
If a tank can be filled by a pipe in 8 hours and emptied by another pipe in 12 hours, how long will it take to fill the tank if both pipes are opened together?
Correct Answer: 24 hours
Step 1: Determine the rate at which the filling pipe works. If it fills the tank in 8 hours, its rate is 1 tank per 8 hours, or 1/8 of the tank per hour.
Step 2: Determine the rate at which the emptying pipe works. If it empties the tank in 12 hours, its rate is 1 tank per 12 hours, or 1/12 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: (1/8) - (1/12).
Step 4: To subtract these fractions, find a common denominator. The least common multiple of 8 and 12 is 24.
Step 5: Convert the rates to have the same denominator: (1/8) = 3/24 and (1/12) = 2/24.
Step 6: Now subtract the two rates: (3/24) - (2/24) = 1/24.
Step 7: The net rate of filling the tank is 1/24 of the tank per hour. This means it takes 24 hours to fill the tank when both pipes are open.
Rate of Work – Understanding how to calculate the combined rate of filling and emptying a tank using the rates of individual pipes.
Fractional Work – Applying the concept of fractions to determine the portion of the tank filled or emptied per hour.
