Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. If both pipes are opened together, how long will it take to fill the tank?
Correct Answer: 7.2 hours
- Step 1: Determine the rate at which pipe A fills the tank. Since it can fill the tank in 12 hours, its rate is 1/12 of the tank per hour.
- Step 2: Determine the rate at which pipe B fills the tank. Since it can fill the tank in 18 hours, its rate is 1/18 of the tank per hour.
- Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/12 + 1/18.
- Step 4: To add 1/12 and 1/18, find a common denominator. The least common multiple of 12 and 18 is 36.
- Step 5: Convert 1/12 to have a denominator of 36. This becomes 3/36.
- Step 6: Convert 1/18 to have a denominator of 36. This becomes 2/36.
- Step 7: Now add the two fractions: 3/36 + 2/36 = 5/36.
- Step 8: The combined rate of both pipes is 5/36 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 (5/36).
- Step 10: The reciprocal of 5/36 is 36/5.
- Step 11: Calculate 36/5 to find the time in hours. This equals 7.2 hours.
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