Question

It takes you 3 hours to drive to a concert 135 miles away. You drive 55 miles per hour on highways and 40 miles per hour on the rest of the roads. Write a system of linear equations that represents this equation. Use x to represent the number of hours driving on a highway and y to represent the number of hours driving on other roads.

Answer 1

x + y = 3 (1)

55x + 40y = 135 (2)

Explanation:

Since x to represent the number of hours driving on a highway and y to represent the number of hours driving on other roads and the total time for driving is 3 hours,

x + y = 3 (1)

Also, You drive 55 miles per hour on highways and 40 miles per hour on the rest of the roads, the distance moved on highways is 55x and the distance moved on the rest of the roads is 40y (since distance = speed × time).

Since the total distance moved is 135 miles, we have

55x + 40y = 135 (2)

So, the system of linear equations that represent the situation is

x + y = 3 (1)

55x + 40y = 135 (2)