A tank is filled by two pipes in 15 and 20 minutes 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 15 and 20 minutes respectively. If both pipes are opened together, how long will it take to fill the tank?

Solution: The combined rate is 1/15 + 1/20 = 7/60. Therefore, time taken = 60/7 ≈ 8.57 minutes.

Steps: 9

Step 1: Determine the rate at which each pipe fills the tank. The first pipe fills the tank in 15 minutes, so its rate is 1/15 of the tank per minute.
Step 2: The second pipe fills the tank in 20 minutes, so its rate is 1/20 of the tank per minute.
Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/15 + 1/20.
Step 4: To add the fractions, find a common denominator. The least common multiple of 15 and 20 is 60.
Step 5: Convert the fractions: 1/15 becomes 4/60 and 1/20 becomes 3/60.
Step 6: Now add the two fractions: 4/60 + 3/60 = 7/60.
Step 7: The combined rate of both pipes is 7/60 of the tank per minute.
Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of the combined rate: 1 / (7/60) = 60/7 minutes.
Step 9: Calculate 60/7, which is approximately 8.57 minutes.