Question

When my wife and I drove to Boston from Chicago (a trip of about 1170 miles), the trip took a total of 20 hours. The first part of the trip, I drove at an average speed of 55 mph. The second part of the trip was driven by my wife, who drove at an average speed of 65 mph. For how many hours did each of us drive?

Answer 1

13 hours

Explanation:

Answer 2

Let's call the time you drove "x" and the time your wife drove "y". We know that the sum of the two times is 20 hours:

x + y = 20

We also know the distance traveled during each part of the trip. The first part of the trip was 55x miles, and the second part of the trip was 65y miles. The total distance of the trip was 1170 miles:

55x + 65y = 1170

We can use the first equation to solve for x in terms of y:

x = 20 - y

We can then substitute this expression for x in the second equation:

55(20 - y) + 65y = 1170

Simplifying and solving for y:

1100 - 55y + 65y = 1170

10y = 70

y = 7

So your wife drove for 7 hours. We can use the first equation to find your driving time:

x + 7 = 20

x = 13

So you drove for 13 hours.