A tank is filled by two pipes A and B in 12 hours and 16 hours respectively. If pipe A is opened for 4 hours and then pipe B is opened, how long will it take to fill the tank?
Practice Questions
1 question
Q1
A tank is filled by two pipes A and B in 12 hours and 16 hours respectively. If pipe A is opened for 4 hours and then pipe B is opened, how long will it take to fill the tank?
8 hours
10 hours
12 hours
14 hours
In 4 hours, A fills 1/3 of the tank. The remaining 2/3 can be filled by A and B together in 4 hours.
Questions & Step-by-step Solutions
1 item
Q
Q: A tank is filled by two pipes A and B in 12 hours and 16 hours respectively. If pipe A is opened for 4 hours and then pipe B is opened, how long will it take to fill the tank?
Solution: In 4 hours, A fills 1/3 of the tank. The remaining 2/3 can be filled by A and B together in 4 hours.
Steps: 7
Step 1: Determine the rate at which pipe A fills the tank. Since pipe A fills the tank in 12 hours, its rate is 1/12 of the tank per hour.
Step 2: Determine the rate at which pipe B fills the tank. Since pipe B fills the tank in 16 hours, its rate is 1/16 of the tank per hour.
Step 3: Calculate how much of the tank pipe A fills in 4 hours. In 4 hours, pipe A fills 4 * (1/12) = 4/12 = 1/3 of the tank.
Step 4: Determine how much of the tank is left to fill after 4 hours. Since 1/3 of the tank is filled, the remaining part is 1 - 1/3 = 2/3 of the tank.
Step 5: Calculate the combined rate of pipes A and B when both are opened. The combined rate is (1/12 + 1/16). To add these, find a common denominator, which is 48. So, (4/48 + 3/48) = 7/48 of the tank per hour.
Step 6: Determine how long it takes for pipes A and B together to fill the remaining 2/3 of the tank. Set up the equation: (7/48) * time = 2/3. Solving for time gives time = (2/3) / (7/48) = (2/3) * (48/7) = 16/7 hours.
Step 7: Convert 16/7 hours into hours and minutes. 16/7 hours is approximately 2 hours and 18 minutes.
