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.
Let the volume be V
at a rate of 125 L/h, time would be V/125 hrs
at a rate of 150 L/h, time would be V/150 hrs
V/125 - V/150 = 1 1/3 = 4/3
times 750
6V - 5V = 1000
V = 1000
But why did you times by 750?
Because when you do v/125 - v/150 = 4/3, both the bottom numbers of the fraction have to be the same and there common denominator happens to be 750.
How the haeck did you get 1 1/3
To determine the volume of the tank, let's break down the problem step by step.
Step 1: Assign variables:
Let:
- V be the volume of the tank (in liters)
- R be the initial delivery rate from the tap (in liters per hour)
- T be the initial time taken to fill the tank (in hours)
- R' be the increased delivery rate from the tap (in liters per hour)
- T' be the decreased time taken to fill the tank with the increased delivery rate (in hours)
Step 2: Set up equations based on the given information:
We are given that the initial delivery rate is 125L/hr, so R = 125.
We are also given that if the delivery rate were increased by 25L/hr (R' = R + 25), the tank would be filled 1 hour and 20 minutes sooner. To convert 1 hour 20 minutes to hours, we divide it by 60, so T' = T - 1.33.
Step 3: Set up an equation relating the variables:
The equation representing the relationship between volume, delivery rate, and time is V = R * T. Since the tank is being filled at a constant rate, this equation holds true for both the initial delivery rate and the increased delivery rate.
So, we have V = R * T and V = R' * T'.
Step 4: Solve the equations:
Substituting the known values into the equations, we have:
V = 125 * T (Equation 1)
V = (125 + 25) * (T - 1.33) (Equation 2)
Simplifying Equation 2, we have:
V = 150 * (T - 1.33)
Now, set Equation 1 equal to Equation 2:
125 * T = 150 * (T - 1.33)
Simplify and solve for T:
125T = 150T - 199.5
25T = 199.5
T = 7.98 hours
Step 5: Calculate the volume:
Substitute the value of T into Equation 1:
V = 125 * 7.98
V = 997.5 liters
Therefore, the volume of the tank is 997.5 liters.