When will you and your friend meet?

Question

You are traveling 75 miles per hour and your friend is traveling 40 miles per hour. However your friend has a 25 mile an hour head start. If you both have about 200 miles to travel when will you meet up with your friend?

Answer 1

Assuming you are traveling in the same direction:

Your friend's location can be modeled by the function f(t) = 40t + 25; your location can be modeled by g(t)= 75t.

We simply need to set these functions equal to each other, so 40t + 25 = 75t, which simplifies to 35t = 25, or t= 5/7 hours. We can then plug that into either equation and get g(5/7) = 53.57 miles. Therefore, you will meet your friend before 200 miles.