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.
1 answer
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.
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.
Answers
Answer:(a) Snow Dome Ski: y = 65 + tMt. Winterpark: y = 74 + ½t(b) Hours greater than 18Step-by-step explanation:GivenSnow Dome SkiBase Snow = 65inRate = 1 in per hourMt. WinterparkBase Snow = 74 inRate = ½ in per hourSolving (a): Equation for bothTo determine the amount of snow (y) at time (t) for any of the two, we make use of:y = Base Snow + Rate * tFor Snow Dome Ski:y = 65 + 1 * ty = 65 + tFor Mt. Winterparky = 74 + ½ * ty = 74 + ½tSolving (b): When snow dome will have more snow.To solve this, we set the following inequalitySnow Dome Ski > Mt. WinterparkThis gives:65 + t > 74 + ½tCollect Like Termst - ½t > 74 - 65½t > 9Multiply both sides by 2t > 18This 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.....
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