Pipe A can fill a tank in 6 hours, while pipe B can fill it in 9 hours. If both pipes are opened together, how long will it take to fill the tank?

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Q: Pipe A can fill a tank in 6 hours, while pipe B can fill it in 9 hours. If both pipes are opened together, how long will it take to fill the tank?

Solution: The combined rate is 1/6 + 1/9 = 5/18. Therefore, it will take 18/5 = 3.6 hours to fill the tank.

Steps: 10

Step 1: Determine the rate at which Pipe A fills the tank. Since Pipe A can fill the tank in 6 hours, its rate is 1 tank per 6 hours, or 1/6 of the tank per hour.
Step 2: Determine the rate at which Pipe B fills the tank. Since Pipe B can fill the tank in 9 hours, its rate is 1 tank per 9 hours, or 1/9 of the tank per hour.
Step 3: Add the rates of both pipes together to find the combined rate. The combined rate is (1/6) + (1/9).
Step 4: To add 1/6 and 1/9, find a common denominator. The least common multiple of 6 and 9 is 18.
Step 5: Convert 1/6 to have a denominator of 18: (1/6) = (3/18).
Step 6: Convert 1/9 to have a denominator of 18: (1/9) = (2/18).
Step 7: Now add the two fractions: (3/18) + (2/18) = (5/18).
Step 8: The combined rate of both pipes is 5/18 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 / (5/18) = 18/5 hours.
Step 10: Simplify 18/5 hours to get 3.6 hours.