A large tank is being filled from a tap delivering water at a rate of 125L/hr. If the delivery rate were increased by 25L/hr the tank would be filled 1 hour and 20 minutes sooner.
Determine the volume of the tank.
v / 125 = [v / (125 + 25)] + 4/3
To determine the volume of the tank, we need to use the information given about the delivery rate of water and the time it takes to fill the tank.
Let's denote the volume of the tank as V liters.
According to the information given, when the tap delivers water at a rate of 125L/hr, it takes a certain amount of time to fill the tank completely. Let's call this time T hours.
Therefore, when the delivery rate is increased by 25L/hr, the new delivery rate becomes (125 + 25) L/hr = 150L/hr.
With the increased delivery rate of 150L/hr, the tank can be filled in (T - 1 hour and 20 minutes). To calculate this time in hours, we convert it to hours by dividing 20 minutes by 60 (1 hour = 60 minutes). Therefore, (1 hour and 20 minutes) equals (1 + (20/60)) hours = 1.33 hours.
So, with the increased delivery rate of 150L/hr, the tank can be filled in (T - 1.33) hours.
Now, to find the volume of the tank V, we can set up a proportion using the delivery rates and the time it takes to fill the tank:
125L/hr / T hours = 150L/hr / (T - 1.33) hours
Cross-multiplying and simplifying the equation, we get:
125L/hr * (T - 1.33) hours = 150L/hr * T hours
125T - 166.25 = 150T
25T = 166.25
T = 6.65
So, it takes approximately 6.65 hours to fill the tank when the delivery rate is 125L/hr.
Now, we can substitute this value back into the equation to find the volume of the tank:
V = 125L/hr * 6.65 hours
V = 831.25L
Therefore, the volume of the tank is 831.25 liters.