Two pipes can fill a tank in 9 hours and 12 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 5.14 hours
- Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 9 hours, so its rate is 1/9 of the tank per hour.
- Step 2: The second pipe fills the tank in 12 hours, so its rate is 1/12 of the tank per hour.
- Step 3: Add the rates of both pipes together to find the combined rate. This is 1/9 + 1/12.
- Step 4: To add 1/9 and 1/12, find a common denominator. The least common multiple of 9 and 12 is 36.
- Step 5: Convert 1/9 to 4/36 and 1/12 to 3/36. Now add them: 4/36 + 3/36 = 7/36.
- Step 6: The combined rate of both pipes is 7/36 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 1 divided by (7/36).
- Step 8: The calculation is 36/7, which equals approximately 5.14 hours.
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