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.

a) 30 mph and 10 mph
b) 45 mph and 15 mph
c) 20 mph and 5 mph
d) 36 mph and 12 mph

Answer 1

Aaron's speed on the freeway is 30 mph and his speed on the mountain road is 10 mph.

Step-by-step explanation:

Let's assume Aaron's speed on the mountain road is x mph. Since his speed on the freeway is 3 times his speed on the mountain road, his speed on the freeway is 3x mph.

From 9:15 to 10:45, Aaron spent 1 hour and 30 minutes on the freeway. So, his distance traveled on the freeway is (1.5 hours) * (3x mph) = 4.5x miles.

From 10:45 to 11:15, Aaron spent 30 minutes on the mountain road. So, his distance traveled on the mountain road is (0.5 hours) * (x mph) = 0.5x miles.

The total distance traveled is 110 miles. Therefore, we can write the equation: 4.5x + 0.5x = 110.

By solving this equation, we find that x = 10 mph, which is Aaron's speed on the mountain road. Therefore, his speed on the freeway is 3x = 3 * 10 = 30 mph.