Thread: Cars

Two cars are approaching an intersection. One is 2 miles south of the intersection and is moving at a constant speed of 30 miles per hour. At the same time, the other car is 3 miles east of the intersection and is moving at a constant speed of 40 miles per hour. Express the distance d between the cars as a function of time t.

HINT GIVEN:

At t = 0, the cars are 2 miles south and 3 miles east of the intersection, respectively.

Hello, blueridge!

Did you make a sketch?

Two cars are approaching an intersection.
One is 2 miles south of the intersection and is moving north at 30 mph.
The other car is 3 miles east of and is moving west at 40 mph.
Express the distance between the cars as a function of time .

Code:

        X  3-40t   B    40t    Q
        * - - - - - * - - - - - *
        |         /
        |       /
  2-30t |     / d
        |   /
        | /
      A *
        |
    30t |
        |
      P *

The first car starts at , 2 miles south of
In hours, it has moved miles north to point
. . Hence: .

The second car starts at , 3 mile east of
In hours, it has moved miles west to point
. . Hence: .

From right triangle , we have: .

So we have: .

. . which simplifies to: .