Question 44544
Since the first car was given a two-hour head start, it traveled 2(40 mi/h) = 80 miles ....
First Car's Rate: 40t + 80
Second Car's Rate: xt
The different of the two car's traveled distance is equal to zero:
40t + 80 - xt = 0
40(16/3) + 80 - (16/3)x = 0
-(16/3)x = -240/3 - 640/3
-(16/3)x = -880/3
x = (880/3)(3/16) = 55
The second car was traveling 55 miles per hour.
Check:
First Car: y = 40x + 80
Second Car: y = 55x
Where 'y' is the distance and 'x' is the time:
-y + 40x = -80
+
y - 55x = 0
-15x = -80
x = 16/3
5 hours and 20 minutes