Pipe A can fill a tank in 6 hours, while pipe B can fill it in 4 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 4 hours. If both pipes are opened together, how long will it take to fill the tank?

Solution: The combined rate is 1/6 + 1/4 = 5/12. Therefore, time taken = 12/5 = 2.4 hours.

Steps: 11

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 4 hours, its rate is 1 tank per 4 hours, or 1/4 of the tank per hour.
Step 3: Add the rates of both pipes together to find the combined rate. This is done by adding 1/6 and 1/4.
Step 4: To add 1/6 and 1/4, find a common denominator. The least common multiple of 6 and 4 is 12.
Step 5: Convert 1/6 to a fraction with a denominator of 12. This gives us 2/12.
Step 6: Convert 1/4 to a fraction with a denominator of 12. This gives us 3/12.
Step 7: Now add the two fractions: 2/12 + 3/12 = 5/12.
Step 8: The combined rate of both pipes is 5/12 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. This means you calculate 1 divided by (5/12).
Step 10: The reciprocal of 5/12 is 12/5 hours.
Step 11: Convert 12/5 hours into a decimal to find the time in hours. 12 divided by 5 equals 2.4 hours.