Acar and a truck left washington, dc traveling in opposite directions. the car traveled 19 miles per hour faster than the truck, and at the end of 8 hours they were 1448 miles apart. what was the average speed of each vehicle?

Let
 x = truck speed
 x + 19 = carriage speed
 by definition we have that distance is equal to the speed by time.
 Therefore, we have then
 1448 = (x + (x + 19)) * (8)
 Rewriting the equation, we have then:
 1448 = (2x + 19) * (8)
 1448 = 16x + 152
 Clearing x
 x = (1448-152) / (16) = 81 mi / h
 x = 81 mi / h (truck speed)
 The speed of the car is:
 x + 19 = 81 + 19 = 100 mi / h
 
 The car's speed is 100 mi / hr
 The truck's speed is 81 mi / hr