) An inlet pipe can fill an empty tank in 5 hours by itself, and an outlet pipe can drain the same tank when full in 7 hours by itself. If the tank is two-thirds full when the valves for both pipes are opened, how many minutes will it take to fill the tank?
To fill the whole tank in x hours,
1/5 - 1/7 = 1/x
but you only have to fill 1/3, so adjust accordingly.
1/5 - 1/7 = 2/35
so to fill full tank, time req = 17.5 hrs
17.5 hrs / 3 = 5 hrs & 50 min, so just to fill 1/3 of the tank, time req is 5 hrs, 50 min
—> 1/3 tank needs to be filled (of 7*5 = 35 units)
—> Both pipes together can do = (7-5) = 2 units/hour
—> ( 35/2*3 = 35/6 hrs = 5hrs 50 minutes = 350 minutes) 🙂
To find out how many minutes it will take to fill the tank, we first need to find the rates at which the inlet and outlet pipes fill or drain the tank.
Let's start by finding the rate at which the inlet pipe fills the tank. We know that the inlet pipe can fill the tank in 5 hours by itself. Therefore, the inlet pipe's filling rate is 1 tank / 5 hours, or 1/5 of a tank per hour.
Now let's find the rate at which the outlet pipe drains the tank. We know that the outlet pipe can drain the tank in 7 hours by itself. Therefore, the outlet pipe's draining rate is 1 tank / 7 hours, or 1/7 of a tank per hour.
When both the valves for the inlet and outlet pipes are opened, the net filling rate of the tank is the difference between the filling rate and the draining rate. Since we want to fill the tank, we subtract the draining rate from the filling rate:
Net filling rate = (1/5) - (1/7) = 2/35 tanks per hour
Given that the tank is initially two-thirds full, we need to calculate the remaining filling fraction. In other words, we need to determine how much more of the tank needs to be filled. Since the tank is already two-thirds full, there is one-third remaining to be filled.
Now that we know the net filling rate and the remaining fraction to fill, we can calculate the time it will take to fill the remaining fraction of the tank. We can use the formula:
Time = Fraction to fill / Net filling rate
Time = (1/3) / (2/35) = (1/3) * (35/2) = 35/6 hour
Since we want to express the time in minutes, we can convert 35/6 hours to minutes:
Time in minutes = (35/6) * 60 = 350/6 = 58 1/3 minutes
Therefore, it will take approximately 58 minutes and 20 seconds to fill the tank when the valves for both the inlet and outlet pipes are opened.