How do I do this calculus related rates problem?

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The discussion focuses on solving a calculus related rates problem involving a trapezoidal trough leaking water at a rate of 0.8 liters per second. The dimensions of the trough are specified: a bottom width of 55 cm, a top width of 85 cm, a height of 25 cm, and a length of 3 m. The goal is to determine the rate of change of the water height when the water depth is 11 cm, utilizing the volume formula \(V=\frac{h}{2}(w+55)300=150h(w+55)\) and establishing a linear relationship between the width \(w\) and the height \(h\).

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Temit96
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Water is leaking from a trough at the rate of 0.8 l/s. The trough has a trapezoidal cross section, where the width at the bottom is 55 cm, at the top is 85cm, and the height is 25 cm. The length of the trough is 3 m.
Find the rate at which the height is changing when the depth of water is 11 cm.
 
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I would use cm as the unit of length and s as the unit of time. At time $t$, let the width of the water's surface in a trapezoidal cross-section be $w$. Let the depth of the water be $h$. So, the volume of water at that time is then:

$$V=\frac{h}{2}(w+55)300=150h(w+55)$$

Now, we want to express $w$ as a function of $h$. We can see it will be a linear relationship, and we know two points on the line. Can you use these two points to find the slope and then the point-slope formula to find this line?
 

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