Two pipes can fill a tank in 4 hours and 6 hours respectively. If both pipes are

Two pipes can fill a tank in 4 hours and 6 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

Two pipes can fill a tank in 4 hours and 6 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 4 hours, so its rate is 1/4 of the tank per hour.
Step 2: The second pipe fills the tank in 6 hours, so its rate is 1/6 of the tank per hour.
Step 3: Add the rates of both pipes together to find the combined rate. This is 1/4 + 1/6.
Step 4: To add 1/4 and 1/6, find a common denominator. The least common multiple of 4 and 6 is 12.
Step 5: Convert 1/4 to 3/12 and 1/6 to 2/12.
Step 6: Now add the two fractions: 3/12 + 2/12 = 5/12.
Step 7: The combined rate of both pipes is 5/12 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 / (5/12) = 12/5 hours.
Step 9: Convert 12/5 hours to a decimal: 12 divided by 5 equals 2.4 hours.

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