Firefighter Practice Exam

If a tanker truck fills in 2 hours and drains in 3 hours, how long does it take to fill the tank if the outlet port is left open?

1. 4.5 hours

2. 5 hours

3. 5.5 hours

4. 6 hours

The correct answer is: 5.5 hours

To determine how long it takes to fill the tank when the outlet port is open, we need to consider the rates at which the tanker truck fills and drains the tank. First, let's establish the filling rate of the tanker truck. If it fills the tank in 2 hours, the filling rate can be expressed as 1 tank per 2 hours, or 0.5 tanks per hour. Next, we examine the draining rate. If the tank drains in 3 hours, the draining rate would be 1 tank per 3 hours, or approximately 0.33 tanks per hour. When both processes occur simultaneously—filling while draining—we must subtract the draining rate from the filling rate to find the net rate of filling the tank. Therefore, the net filling rate is: 0.5 tanks per hour (filling rate) - 0.33 tanks per hour (drainage rate) = 0.17 tanks per hour. To find out how long it takes to fill one tank at this net rate, we take the reciprocal of the filling rate: 1 tank ÷ 0.17 tanks per hour = approximately 5.88 hours. When rounding this to the nearest half hour, it most accurately falls