how long until they are at the same point?

Question

Jim and Beth are making the same trip in separate cars. Jim has already traveled 126 miles. He is traveling at a constant rate of 50 miles per hour. Beth has already traveled 62 miles. She is traveling at a constant rate of 58 miles per hour. 

Answer 1

We can write two distance equations for Jim and Beth using their initials as functions of time t.

J(t)=126+50t, B(t)=62+58t.

When they are at the same point, J(t)=B(t), so:

126+50t=62+58t, 64=8t, so t=8 hours. (526 miles from the starting point.)