Three pipes can fill a tank in 6, 8, and 12 hours respectively. If all three pipes are opened together, how long will it take to fill the tank?

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Q: Three pipes can fill a tank in 6, 8, and 12 hours respectively. If all three pipes are opened together, how long will it take to fill the tank?

Solution: The combined rate is 1/6 + 1/8 + 1/12 = 1/3. Therefore, it will take 3 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 6 hours, so its rate is 1/6 of the tank per hour.
Step 2: The second pipe fills the tank in 8 hours, so its rate is 1/8 of the tank per hour.
Step 3: The third pipe fills the tank in 12 hours, so its rate is 1/12 of the tank per hour.
Step 4: Add the rates of all three pipes together: 1/6 + 1/8 + 1/12.
Step 5: To add these fractions, find a common denominator. The least common multiple of 6, 8, and 12 is 24.
Step 6: Convert each fraction to have the common denominator of 24: 1/6 = 4/24, 1/8 = 3/24, and 1/12 = 2/24.
Step 7: Now add the fractions: 4/24 + 3/24 + 2/24 = 9/24.
Step 8: Simplify 9/24 to 3/8. This means together, the pipes fill 3/8 of the tank in one hour.
Step 9: To find out how long it takes to fill the entire tank, take the reciprocal of 3/8, which is 8/3 hours.
Step 10: Convert 8/3 hours into hours and minutes. 8/3 hours is 2 hours and 40 minutes.