A tank can be filled by a pipe in 6 hours and emptied by another pipe in 8 hours. If both pipes are opened together, how long will it take to fill the tank? (2020)
Practice Questions
1 question
Q1
A tank can be filled by a pipe in 6 hours and emptied by another pipe in 8 hours. If both pipes are opened together, how long will it take to fill the tank? (2020)
12 hours
24 hours
48 hours
18 hours
Rate of filling = 1/6 tank/hour, Rate of emptying = 1/8 tank/hour. Combined rate = 1/6 - 1/8 = 1/24 tank/hour. Time = 1 / (1/24) = 24 hours.
Questions & Step-by-step Solutions
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Q
Q: A tank can be filled by a pipe in 6 hours and emptied by another pipe in 8 hours. If both pipes are opened together, how long will it take to fill the tank? (2020)
Solution: Rate of filling = 1/6 tank/hour, Rate of emptying = 1/8 tank/hour. Combined rate = 1/6 - 1/8 = 1/24 tank/hour. Time = 1 / (1/24) = 24 hours.
Steps: 6
Step 1: Determine the rate at which the filling pipe works. It fills the tank in 6 hours, so the rate is 1 tank per 6 hours, which is 1/6 tank per hour.
Step 2: Determine the rate at which the emptying pipe works. It empties the tank in 8 hours, so the rate is 1 tank per 8 hours, which is 1/8 tank per hour.
Step 3: Calculate the combined rate when both pipes are opened together. Since one pipe fills and the other empties, we subtract the emptying rate from the filling rate: 1/6 - 1/8.
Step 4: To subtract the fractions, find a common denominator. The common denominator for 6 and 8 is 24. Convert the rates: 1/6 = 4/24 and 1/8 = 3/24.
Step 5: Now subtract the two rates: 4/24 - 3/24 = 1/24 tank per hour.
Step 6: To find out how long it takes to fill the tank at the combined rate, take the reciprocal of the combined rate: 1 / (1/24) = 24 hours.
