A tank is filled by two pipes A and B in 15 hours and 20 hours respectively. If both pipes are opened together, 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 15 hours and 20 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
8 hours
10 hours
12 hours
15 hours
The combined rate is 1/15 + 1/20 = 7/60. Therefore, it will take 60/7 hours to fill the tank.
Questions & Step-by-step Solutions
1 item
Q
Q: A tank is filled by two pipes A and B in 15 hours and 20 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
Solution: The combined rate is 1/15 + 1/20 = 7/60. Therefore, it will take 60/7 hours to fill the tank.
Steps: 7
Step 1: Determine the rate at which pipe A fills the tank. Since it fills the tank in 15 hours, its rate is 1/15 of the tank per hour.
Step 2: Determine the rate at which pipe B fills the tank. Since it fills the tank in 20 hours, its rate is 1/20 of the tank per hour.
Step 3: Add the rates of both pipes to find the combined rate. This is done by calculating 1/15 + 1/20.
Step 4: To add 1/15 and 1/20, find a common denominator. The least common multiple of 15 and 20 is 60.
Step 5: Convert 1/15 to 4/60 and 1/20 to 3/60. Now add them: 4/60 + 3/60 = 7/60.
Step 6: The combined rate of both pipes is 7/60 of the tank per hour.
Step 7: To find out how long it takes to fill the tank, take the reciprocal of the combined rate. This means you calculate 60/7 hours.
