CCSS.MATH.CONTENT.8.EE.C.8.C – Solve real-world and mathematical problems leading to two linear equations in two variables

The following is an example from one  of my worksheets I am developing aligning with Common Core standard 8.EE.C.8.c. (That and it is a fun one about driving out West!)

Timmy and Sarah are living in Belmont, Massachusetts. They decide to drive to Vail, Colorado for the start of the ski season. Vail is 2,064 miles away from Belmont. Timmy and Sarah both have their own cars. Timmy leaves Belmont two days before Sarah but stops for a day midway to work on his car. If Timmy averages 55 miles per hour and drives 10 hours a day and Sarah averages 75 mph and drives 11 hours a day, will Sarah catch up to Timmy, and if so when?”

To solve:

Set up a distance equation for Timmy:
d = 550(x – 1) (because he travels 55 x 10 miles per day and x represents the days driving since Timmy’s trip began)

Set up a distance equation for Sarah:
d = 825(x – 2) (because she travels 75 x 11 miles per day and she started two days after Timmy started)

Set the distance equations equal to one another:
550(x – 1) = 825(x -2) and solve for x, x = 4. So Sarah catches up with Timmy four days after Timmy began the trip and before he gets to Colorado.

A great activity for this would be to integrate Geography into the lesson and find where Sarah catches Timmy, which would be about midway through Nebraska (using Google maps).