Question

There was no snow on the ground when it started falling at midnight at a constant rate of 1.5 inches per hour. At

Answer 1

Answer:

$x=\frac{14}{3}$ hours after midnight or at 4:40 am the depth of the snow on the ground was 8 inches.

Step-by-step explanation:

Consider the provided information.

Let x represents the number of hours and S(x) represents the depth of snow.

There was no snow on the ground when it started falling at midnight at a constant rate of 1.5 inches per.

That means the depth of snow will be:

$S(x)=1.5x\ \ \ 0\leq x< 4$

At  4:00 a.m., it starting falling at a constant rate of 3 inches per hour,

$S(x)=3(x-4)+6\ \ \ 4\leq x$

7:00 a.m. to 9:00 a.m., snow was  falling at a constant rate of 2 inches per hour.

$S(x)=2(x-7)+15\ \ \ 7\leq x\leq 9$

The required piece-wise linear function is

$\left\{\begin{matrix}1.5x & 0\leq x$

Now we need to find When was the depth of the snow on the ground 8 inches?

Substitute S(x)=8 in $S(x)=3(x-4)+6$

$8=3(x-4)+6$

$2=3(x-4)$

$\frac{2}{3}=x-4$

$\frac{2+12}{3}=x$

$x=\frac{14}{3}$

$x=\frac{14}{3}$ hours after midnight or at 4:40 am the depth of the snow on the ground was 8 inches.