Question

A student drove the 1 245 km from Edmonton to Vancouver in 16.5 hours. This included a one hour

stop for lunch and a 30 min stop for fuel. She averaged 100 km/h on the divided highways and
75 km/h on the non-divided highways. How much time did she spend on the divided highway?

Answer 1

The student spent 4.8 hours on the divided highway, which was calculated by solving a system of equations derived from the total travel time and the average speeds on different types of highways.

Step-by-step explanation:

To answer the question: How much time did the student spend on the divided highway, we can calculate it using the given speeds on different types of highways and the total travel time, excluding stops.

The student's total driving time, excluding stops (1 hour for lunch and 30 minutes for fuel), was 16.5 hours - 1 hour - 0.5 hours = 15 hours.

Let x be the time spent on divided highways at 100 km/h and y be the time spent on non-divided highways at 75 km/h. We have two equations based on the average speeds and the distances covered:

1. x + y = 15 (Total time spent driving)
2. 100x + 75y = 1245 km (Total distance covered)

Solving the system of equations, we can find out the values of x and y.

From equation (1), y = 15 - x.

Substitute y in equation (2):

100x + 75(15 - x) = 1245

100x + 1125 - 75x = 1245

25x = 120

x = 120 / 25

x = 4.8 hours

The student spent 4.8 hours on the divided highway.