# 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.

**Solution 03**

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Volume of water:

$V = 10(3)y = 30y$

$\dfrac{dV}{dt} = 30 \dfrac{dy}{dt}$

$12 = 30 \dfrac{dy}{dt}$

$\dfrac{dy}{dt} = 0.4 \,\, \text{ ft/min}$ *answer*