Math Problem Statement
A large tank of height 10 m is fitted with an inlet pipe which can fill the tank in 60 minutes. The tank has three emptying outlets pipes fitted at the heights of 5 m, & m and 9.5 m respectively from the bottom. All the pipes are opened simultaneously with the tank being empty initially. In how much time (in minutes) will 95% of the tank be filled, if the lowest outlet pipe alone can empty half the tank in one and a half hour, the outlet pipe in the middle alone can empty 20% of the tank in 1 hour 12 minutes and the outlet pipe at the top alone can empty 5% of the tank in 18 minutes?
Solution
To solve the problem, we will break down the process into smaller steps.
Step 1: Find the filling rate of the inlet pipe.
The inlet pipe fills the tank in 60 minutes. Therefore, the rate at which the inlet pipe fills the tank is:
[ \text{Filling rate} = \frac{1 \text{ tank}}{60 \text{ minutes}} = \frac{1}{60} \text{ tank per minute}.
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Math Problem Analysis
Mathematical Concepts
Rate of Work
Volume Calculations
Simultaneous Equations
Formulas
Filling rate = (Tank filled) / (Time)
Emptying rate = (Tank emptied) / (Time)
Combined rates = Inlet rate - (Sum of outlet rates)
Theorems
Work Rate Theorem
Suitable Grade Level
Grades 10-12
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