Two pipes can fill a tank in 10 hours and 15 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

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Q: Two pipes can fill a tank in 10 hours and 15 hours respectively. If both pipes are opened together, how long will it take to fill the tank?

Solution: The combined rate is 1/10 + 1/15 = 1/6. Therefore, it will take 6 hours to fill the tank.

Steps: 8

Step 1: Understand that each pipe has a filling rate. The first pipe fills the tank in 10 hours, so its rate is 1/10 of the tank per hour.
Step 2: The second pipe fills the tank in 15 hours, so its rate is 1/15 of the tank per hour.
Step 3: To find the combined rate of both pipes, add their rates together: 1/10 + 1/15.
Step 4: To add the fractions, find a common denominator. The least common multiple of 10 and 15 is 30.
Step 5: Convert the fractions: 1/10 becomes 3/30 and 1/15 becomes 2/30.
Step 6: Now add the fractions: 3/30 + 2/30 = 5/30.
Step 7: Simplify 5/30 to 1/6. This means together, both pipes fill 1/6 of the tank in one hour.
Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of 1/6, which is 6 hours.