A tank is filled by two pipes in 8 hours and 12 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 8 hours and 12 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

Solution: The combined rate is 1/8 + 1/12 = 5/24. Therefore, it will take 24/5 = 4.8 hours to fill the tank.

Steps: 9

Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 8 hours, so its rate is 1/8 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 1/8 + 1/12.
Step 4: To add 1/8 and 1/12, find a common denominator. The least common multiple of 8 and 12 is 24.
Step 5: Convert 1/8 to 3/24 and 1/12 to 2/24.
Step 6: Now add the two fractions: 3/24 + 2/24 = 5/24.
Step 7: The combined rate of both pipes is 5/24 of the tank per hour.
Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of the combined rate: 1 / (5/24) = 24/5 hours.
Step 9: Calculate 24/5, which equals 4.8 hours.