Sam left at 12:00 (noon) travelling 55 mph. Will left at 1:00 pm travelling 75 mph How far will they have traveled when Will catches up to Sam?

Question

Write an equation to model when their distances are equal.

 

 

 

Solve the equation. Be sure to show all of your work.

Answer 1

This is a D-I-R-T (Distance-Is-Rate-times-Time) problem.  In such problems one variable is often the same and another is related somehow so we can solve the problem.  In this problem, the distance is equal and one time is 1 hour less than the other.

Let T = time in hours since noon

 

Sam’s distance:     D = 55T

Will’s distance:      D = 75(T-1)

 

Same distance:    55T = 75(T-1)

                     55T = 75T – 75                  [distribute]

                     -20T = -75                 [subtract 75T from both sides]

                       T = 3.75                 [divide both sides by (-20)]

 

Will catches up to Sam at 3.75 hours after noon   (note: that’s 3 hours 45 minutes, or 3:45 PM).

 

Note that we first had to calculate the time.  Now, we can find the distance using either formula:

           D=55(3.75)

           D= 206.25 miles