Question

Snow Dome Ski Resort has 65 inches of snow. It is currently snowing there at a rate of 1 inch per hour. Mt. Winterpark Ski Resort has 74 inches of snow. Currently it is snowing there at a rate of ½ inch per hour.

a) Write equations that show the amount of snow at each resort as a function of the number of hours of snow.

b) If the snow continues at this rate, when will Snow Dome have more snow than Mt. Winterpark? Show your solution process clearly.

Answer 1

To find when Snow Dome will have more snow than Mt. Winterpark, we need to set up and solve the equation: 65 + 1x > 74 + 0.5x. This means that Snow Dome will have more snow than Mt. Winterpark after 18 hours of snowfall.

Step-by-step explanation:

a) Equations:

Let x represent the number of hours of snow.

For Snow Dome Ski Resort: snow depth = 65 + 1x.

For Mt. Winterpark Ski Resort: snow depth = 74 + 0.5x.

b) Snow Depth Comparison:

To find when Snow Dome will have more snow than Mt. Winterpark, we need to set up and solve the equation:

65 + 1x > 74 + 0.5x

Subtract 0.5x from both sides:

0.5x > 9

Divide both sides by 0.5:

x > 18

This means that Snow Dome will have more snow than Mt. Winterpark after 18 hours of snowfall.

Answer 2

(a)

Snow Dome Ski: y = 65 + t

Mt. Winterpark: y = 74 + ½t

(b) Hours greater than 18

Step-by-step explanation:

Given

Snow Dome Ski

Base Snow = 65in

Rate = 1 in per hour

Mt. Winterpark

Base Snow = 74 in

Rate = ½ in per hour

Solving (a): Equation for both

To determine the amount of snow (y) at time (t) for any of the two, we make use of:

y = Base Snow + Rate * t

For Snow Dome Ski:

y = 65 + 1 * t

y = 65 + t

For Mt. Winterpark

y = 74 + ½ * t

y = 74 + ½t

Solving (b): When snow dome will have more snow.

To solve this, we set the following inequality

Snow Dome Ski > Mt. Winterpark

This gives:

65 + t > 74 + ½t

Collect Like Terms

t - ½t > 74 - 65

½t > 9

Multiply both sides by 2

t > 18

This implies that the snow at Snow Dome Ski will be more than the snow at Mt. Winterpark after 18 hours.

After 18 hours means, hours greater than 18 which could be 19, 20, 21.....