A tank is filled by two pipes in 12 hours and 16 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

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Q: A tank is filled by two pipes in 12 hours and 16 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

Solution: The combined rate is 1/12 + 1/16 = 7/48. Therefore, it will take 48/7 hours to fill the tank.

Steps: 10

Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 12 hours, so its rate is 1/12 of the tank per hour.
Step 2: The second pipe fills the tank in 16 hours, so its rate is 1/16 of the tank per hour.
Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/12 + 1/16.
Step 4: To add 1/12 and 1/16, find a common denominator. The least common multiple of 12 and 16 is 48.
Step 5: Convert 1/12 to a fraction with a denominator of 48: (1/12) * (4/4) = 4/48.
Step 6: Convert 1/16 to a fraction with a denominator of 48: (1/16) * (3/3) = 3/48.
Step 7: Now add the two fractions: 4/48 + 3/48 = 7/48.
Step 8: The combined rate of both pipes is 7/48 of the tank per hour.
Step 9: To find out how long it takes to fill the tank, take the reciprocal of the combined rate: 1 / (7/48) = 48/7 hours.
Step 10: Therefore, it will take 48/7 hours to fill the tank when both pipes are opened together.