# Time Rates

## 04-05 Water flowing into triangular trough

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## 03 Water flowing into rectangular trough

**Problem 03**

A rectangular trough is 10 ft long and 3 ft wide. Find how fast the surface rises, if water flows in at the rate of 12 ft^{3}/min.

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## 01-02 Water flowing into cylindrical tank

**Problem 01**

Water is flowing into a vertical cylindrical tank at the rate of 24 ft^{3}/min. If the radius of the tank is 4 ft, how fast is the surface rising?

**Problem 02**

Water flows into a vertical cylindrical tank at 12 ft^{3}/min, the surface rises 6 in/min. Find the radius of the tank.

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## Time Rates | Applications

**Time Rates**

If a quantity x is a function of time t, the time rate of change of x is given by dx/dt.

When two or more quantities, all functions of t, are related by an equation, the relation between their rates of change may be obtained by differentiating both sides of the equation with respect to t.

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