Question

Aaron left at 9:15 to drive to his mountain cabin 110 miles away. He drove on the freeway until 10:45 and then he drove on the mountain road. He arrived at 11:15. His speed on the freeway was 3 times his speed on the mountain road. Find Aaron’s speed on the freeway and on the mountain road.

Answer 1

Aaron's speed on the freeway is 90 miles per hour and his speed on the mountain road is 30 miles per hour.

Step-by-step explanation:

To find Aaron's speed on the freeway and mountain road, we can use the distance = speed × time formula. Let's first find the time spent on the freeway. Aaron left at 9:15 and arrived at 10:45, so the time spent on the freeway is 1 hour and 30 minutes (10:45 - 9:15 = 1 hour and 30 minutes). The distance traveled on the freeway is 110 miles. Let's assume the speed on the mountain road is x miles per hour and the speed on the freeway is 3x miles per hour.

Using the formula for distance = speed × time, we can set up the following equations:

1. 110 = 3x × 1.5 (converted 1 hour 30 minutes to 1.5 hours)
2. 110 = x × 0.5 (the time spent on the mountain road is 0.5 hours)

Solving these equations, we find that x = 30 miles per hour, so Aaron's speed on the freeway is 3x = 3 × 30 = 90 miles per hour and his speed on the mountain road is x = 30 miles per hour.