If a tank can be filled by a pipe in 20 minutes and emptied by another pipe in 3
Practice Questions
Q1
If a tank can be filled by a pipe in 20 minutes and emptied by another pipe in 30 minutes, how long will it take to fill the tank if both pipes are opened together?
10 minutes
15 minutes
20 minutes
25 minutes
Questions & Step-by-Step Solutions
If a tank can be filled by a pipe in 20 minutes and emptied by another pipe in 30 minutes, how long will it take to fill the tank if both pipes are opened together?
Correct Answer: 60 minutes
Step 1: Determine the rate at which the filling pipe works. If it fills the tank in 20 minutes, its rate is 1 tank per 20 minutes, or 1/20 tanks per minute.
Step 2: Determine the rate at which the emptying pipe works. If it empties the tank in 30 minutes, its rate is 1 tank per 30 minutes, or 1/30 tanks per minute.
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 common 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 is 1/60 tanks per minute.
Step 7: To find out how long it takes to fill the tank at this net rate, take the reciprocal of the net rate: 1 / (1/60) = 60 minutes.
Rate of Work – Understanding how to calculate the rate at which a tank is filled or emptied by different pipes.
Combined Rates – Calculating the net effect of multiple rates working together, such as filling and emptying simultaneously.
