If a tank can be filled by a pipe in 20 hours and emptied by another pipe in 30 hours, how long will it take to fill the tank if both pipes are opened together?
Practice Questions
1 question
Q1
If a tank can be filled by a pipe in 20 hours and emptied by another pipe in 30 hours, how long will it take to fill the tank if both pipes are opened together?
12 hours
15 hours
18 hours
24 hours
The net rate is 1/20 - 1/30 = 1/60. Therefore, it will take 60 hours to fill the tank.
Questions & Step-by-step Solutions
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Q
Q: If a tank can be filled by a pipe in 20 hours and emptied by another pipe in 30 hours, how long will it take to fill the tank if both pipes are opened together?
Solution: The net rate is 1/20 - 1/30 = 1/60. Therefore, it will take 60 hours to fill the tank.
Steps: 7
Step 1: Determine the rate at which the filling pipe works. If it fills the tank in 20 hours, its rate is 1 tank per 20 hours, or 1/20 of the tank per hour.
Step 2: Determine the rate at which the emptying pipe works. If it empties the tank in 30 hours, its rate is 1 tank per 30 hours, or 1/30 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: (1/20) - (1/30).
Step 4: To subtract these fractions, find a common denominator. The least common multiple of 20 and 30 is 60.
Step 5: Convert the rates to have the same denominator: (1/20) = (3/60) and (1/30) = (2/60).
Step 6: Now subtract the two rates: (3/60) - (2/60) = (1/60). This means the net rate of filling the tank is 1/60 of the tank per hour.
Step 7: To find out how long it takes to fill the entire tank at this rate, take the reciprocal of the net rate: 1 / (1/60) = 60 hours.
