Question 330782
You know that D=VT, where D=distance, V=velocity (speed) and T = time.


Rearranging for time, we have D/V = T


We know that their times are the same, so Cathy's time = Dave's time

Tc = Td
Dc/Vc = Dd/Vd


Where Dc=Cathy's distance when they meet, Vc = Cathy's velocity, and so on...


We know that Dc+Dd = 80, (or Dc =80-Dd) because they start 80 miles apart and are heading towards each other.


Put in what you know:

Dc/14 = Dd/18
80-Dd/14 = Dd/18


Solve for Dd by cross multiplying:


18(80-Dd) = 14Dd
32Dd = 1440
Dd = 45


So Dave travels 45 miles. Now find his time:


T = Dd/Vd
T = 45/18
T = 2.5


So they will meet after 2.5 hours. You can solve for T in the equation for Cathy, and it will be the same.