If a tank is filled by a pipe in 5 hours and another pipe can empty it in 10 hou
Practice Questions
Q1
If a tank is filled by a pipe in 5 hours and another pipe can empty it in 10 hours, how long will it take to fill the tank if both pipes are opened for 2 hours?
1 hour
2 hours
3 hours
4 hours
Questions & Step-by-Step Solutions
If a tank is filled by a pipe in 5 hours and another pipe can empty it in 10 hours, how long will it take to fill the tank if both pipes are opened for 2 hours?
Step 1: Determine how much of the tank the filling pipe fills in 1 hour. Since it fills the tank in 5 hours, it fills 1/5 of the tank in 1 hour.
Step 2: Calculate how much of the tank the filling pipe fills in 2 hours. In 2 hours, it fills 2/5 of the tank (2 * 1/5).
Step 3: Determine how much of the tank the emptying pipe empties in 1 hour. Since it empties the tank in 10 hours, it empties 1/10 of the tank in 1 hour.
Step 4: Calculate how much of the tank the emptying pipe empties in 2 hours. In 2 hours, it empties 2/10 of the tank, which simplifies to 1/5 of the tank (2/10 = 1/5).
Step 5: Find the net amount of the tank filled after 2 hours. Subtract the amount emptied from the amount filled: 2/5 (filled) - 1/5 (emptied) = 1/5 of the tank is filled.
Step 6: Since 1/5 of the tank is filled after 2 hours, determine how much time it will take to fill the remaining 4/5 of the tank using the filling pipe alone.
Step 7: The filling pipe fills 1/5 of the tank in 1 hour, so to fill 4/5 of the tank, it will take 4 hours (4 * 1 hour).
Step 8: Add the 2 hours already spent to the 4 hours needed to fill the remaining part. Total time = 2 hours + 4 hours = 6 hours.
