David is 168 miles away from Cesar. They are traveling towards each other. If Cesar travels 8 mph faster than David and they meet after 7 hours, how fast was each traveling?

Answer 1

Ty, here's how to answer this one.

We need the standard equation: s = vt where s = distance traveled, v = speed, and t = time

Suppose David is traveling in the positive x-direction, i.e., to the right, at speed be v

Then, Cesar is traveling in the negative x-direction, i.e., to the right at speed = -(v + 8). The minus sign indicates Cesar is graveling to the left.

Their net speed of approach is v - (-(v + 8)) = v + (v + 8) = 2v + 8

Plug this into the first equation above: 168 = (2v + 8) 7

24 = 2v + 8

16 = 2v

v = 8 mph

Answer: David's speed = 8 mph and Cesar's = 16 mph