Question

Mr. Jones wants to place a chimney on his roof. It is recommended that the chimney be set at a height of at least 30 feet. The height of the roof is described by the function f(x)=−4/3|x−10| + 40 where x is the distance along the width of the roof. Where should Leroy place the chimney if the house is 45 feet wide?

Answer 1

The distance at which the chimney is to be installed is required.

The chimney can be installed is at either 17.5 feet or 2.5 feet along the width of the roof.

The height of the roof is given by the function

$f(x)=-\dfrac{4}{3}|x-10|+40$

where, x is the distance along the width of the roof

The height of the chimney is at least 30 feet, so

$30=-\dfrac{4}{3}|x-10|+40\\\Rightarrow 30-40=-\dfrac{4}{3}|x-10|\\\Rightarrow -10\times -\dfrac{3}{4}=|x-10|\\\Rightarrow |x-10|=7.5$

$\\\Rightarrow x-10=7.5\\\Rightarrow x=17.5$

or

$x-10=-7.5\\\Rightarrow x=2.5$

So, the chimney can be installed at 17.5 feet or 2.5 feet.

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