A tank can be filled by a pipe in 15 hours and emptied by another pipe in 25 hours. If both pipes are opened together, how long will it take to fill the tank?
Practice Questions
1 question
Q1
A tank can be filled by a pipe in 15 hours and emptied by another pipe in 25 hours. If both pipes are opened together, how long will it take to fill the tank?
10 hours
12 hours
15 hours
20 hours
The net rate is 1/15 - 1/25 = 1/75. Therefore, it will take 75 hours to fill the tank.
Questions & Step-by-step Solutions
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Q
Q: A tank can be filled by a pipe in 15 hours and emptied by another pipe in 25 hours. If both pipes are opened together, how long will it take to fill the tank?
Solution: The net rate is 1/15 - 1/25 = 1/75. Therefore, it will take 75 hours to fill the tank.
Steps: 8
Step 1: Determine the rate at which the filling pipe works. It fills the tank in 15 hours, so its rate is 1 tank per 15 hours, or 1/15 of the tank per hour.
Step 2: Determine the rate at which the emptying pipe works. It empties the tank in 25 hours, so its rate is 1 tank per 25 hours, or 1/25 of the tank per hour.
Step 3: Calculate the net rate when both pipes are opened together. This is done by subtracting the emptying rate from the filling rate: (1/15) - (1/25).
Step 4: To subtract these fractions, find a common denominator. The least common multiple of 15 and 25 is 75.
Step 5: Convert the rates to have the common denominator of 75: (1/15 = 5/75) and (1/25 = 3/75).
Step 6: Now subtract the two rates: (5/75) - (3/75) = (5 - 3)/75 = 2/75.
Step 7: The net rate of filling the tank is 2/75 of the tank per hour.
Step 8: To find out how long it takes to fill the entire tank, take the reciprocal of the net rate: 1 / (2/75) = 75/2 = 37.5 hours.
