Question

Increases in snow levels are recorded with positive numbers. Decreases in snow levels are recorded with negative numbers. After a winter storm, the depth of the snow on Cherry Street was 10 \text{ cm}10 cm10, start text, space, c, m, end text. But then, the snow started melting at a rate of \dfrac{1}{3} \text{ cm} 3 1 ​ cmstart fraction, 1, divided by, 3, end fraction, start text, space, c, m, end text per hour. What was the depth of the snow on Cherry Street after 333 hours?

Answer 1

Question:

Increases in snow levels are recorded with positive numbers. Decreases in snow levels are recorded with negative numbers.

After a winter storm, the depth of the snow on Cherry Street was

10 cm. But then, the snow started melting at a rate of 1/3 cm

per hour.

What was the depth of the snow on Cherry Street after 3

hours?

Answer:

The depth of the snow on Cherry Street after 3 hours is 9 cm

Step-by-step explanation:

Here we have

Initial depth of snow = 10 cm

Rate at which the snow melts  = 1/3 cm/hour

Decrease in depth of snow after 3 hours = 3 hour × 1/3 cm/hour = 1 cm

Since decrease in the depth of snow is recorded with negative number, we have;

The decrease in depth of snow after 3 hours = -1 cm

Therefore the depth of the snow after 3 hours is given by;

Depth of snow + change in snow level after 3 hours

= Depth of snow + Decrease in depth of snow after 3 hours (-1)

(Initial depth of snow - Level of snow melted in 3 hours)

= 10 cm - 1 cm = 9 cm

Which gives the depth of snow after 3 hours = 9 cm.

Answer 2

The depth of snow is an illustration of a linear function

The depth of snow after 3 hours is 9cm

The given parameters are:

$Initial = 10cm$

$Rate = -\frac 13cm/hr$ --- it is negative because the amount of snow decreases with time.

The equation that represents the amount of snow in time (t) is:

$f(t) = Initial + Rate \times t$

So, we have:

$f(t) = 10 -\frac 13\times t$

$f(t) = 10 -\frac 13t$

After 3 hours, the value of t is 3.

So, the equation becomes

$f(3) = 10 -\frac 13 \times 3$

$f(3) = 10 -1$

$f(3) = 9$

Hence, the depth of snow after three hours is 9cm

Read more about linear equations at:

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