Question

Snow Dome Ski Resort has 75 inches of snow. It is currently snowing there at a rate of 1 inch per hour. Mt. Winterpark Ski Resort has 68 inches of snow. Currently it is snowing there at a rate of 2 inches per hour.

a) Make a table or a graph showing the amount of snow from 0 to 10 hours at each resort if the snow continues falling at this rate.

b) Indicate on your table or graph where the amount of snow will be the same at both resorts.

Answer 1

a. See explanation for table

b. The 7th hour

Explanation:

Given

Ski Resort

`Base\ Snow = 75in`

`Rate = 1in` hourly

Mt. Winterpark

`Base\ Snow = 68in`

`Rate = 2in` hourly

First, we need to illustrate the amount of snow as an equation in both cases.

`Amount = Base\ Snow + Rate * Time`

Let x be number of hours. and y be the amount of snow

So:

Ski Resort

`y= 75 + 1* x`

`y= 75 + x`

Mt. Winterpark

`y= 68 + 2 * x`

`y= 68 + 2x`

Next, we make a table to show the data.

When
`x = 0`

Ski Resort:
`y = 75 + 0 = 75`

Mt. Winterpark:
`y = 68 + 2(0) = 68`

When
`x = 1`

Ski Resort:
`y = 75 + 1 = 76`

Mt. Winterpark:
`y = 68 + 2(1) = 70`

When
`x = 2`

Ski Resort:
`y = 75 + 2 = 77`

Mt. Winterpark:
`y = 68 + 2(2) = 72`

When
`x = 3`

Ski Resort:
`y = 75 + 3 = 78`

Mt. Winterpark:
`y = 68 + 2(3) = 74`

When
`x = 4`

Ski Resort:
`y = 75 + 4 = 79`

Mt. Winterpark:
`y = 68 + 2(4) = 76`

When
`x = 5`

Ski Resort:
`y = 75 + 5 = 80`

Mt. Winterpark:
`y = 68 + 2(5) = 78`

When
`x = 6`

Ski Resort:
`y = 75 + 6 = 81`

Mt. Winterpark:
`y = 68 + 2(6) = 80`

When
`x = 7`

Ski Resort:
`y = 75 + 7 = 82`

Mt. Winterpark:
`y = 68 + 2(7) = 82`

When
`x = 8`

Ski Resort:
`y = 75 + 8 = 83`

Mt. Winterpark:
`y = 68 + 2(8) = 84`

When
`x = 9`

Ski Resort:
`y = 75 + 9 = 84`

Mt. Winterpark:
`y = 68 + 2(9) = 86`

When
`x = 10`

Ski Resort:
`y = 75 + 10 = 85`

Mt. Winterpark:
`y = 68 + 2(10) = 88`

Hence, the table is:

x ---- Ski Resort ---- Mt. Winterpark

0 --------75 ----------- 68

1 --------76 ----------- 70

2 --------77 ----------- 72

3 --------78 ----------- 74

4 --------79 ----------- 76

5 --------80 ----------- 78

6 --------81 ----------- 80

7 --------82 ----------- 82

8 --------83 ----------- 84

9 --------84 ----------- 86

10 -------85 ----------- 88

(b)

From the table, the amount of snow is the same at the 7th hour and the snow is 82 inches