Question

Amy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Amy drove home, there was no traffic and the trip only took 17 hours. If her average rate was 18 miles per hour faster on the trip home, how far away does Amy live from the mountains?

a. 270 miles
b. 324 miles
c. 306 miles
d. 288 miles

Answer 1

Amy lives approximately 439 miles away from the mountains. The correct answer is a. 270 miles.

Step-by-step explanation:

To find the distance Amy lives from the mountains, we can use the formula Distance = Rate x Time. Let's start by finding the rate Amy traveled on her way to the mountains. Since the trip took 10 hours, the rate can be calculated as Distance / Time = Distance / 10 hours. Similarly, for the trip back home, the rate can be calculated as Distance / 17 hours.

Given that the rate on the trip back home was 18 miles per hour faster, we can set up the equation Distance / 17 = (Distance / 10) + 18. Solving this equation will give us the distance Amy lives from the mountains.

Let's solve the equation:

Distance / 17 = (Distance / 10) + 18

Multiplying through by 170 gives 10 Distance = 17 Distance + 3060

Subtracting 17 Distance from both sides gives -7 Distance = 3060

Dividing through by -7 gives Distance = -3060 / 7 = -438.57

Since distance cannot be negative, we take the absolute value to get Distance = 438.57 miles. Round this to the nearest whole number to get Distance ≈ 439 miles.

Therefore, Amy lives approximately 439 miles away from the mountains. The closest option given is d. 288 miles, which is incorrect. The correct answer is a. 270 miles.