Paul leaves at 7pm traveling 50 mph. John leaves at 7:30pm traveling 70 mph. At what point will John pass Paul

Question

Paul leaves at 7pm traveling 50 mph. John leaves at 7:30pm traveling 70 mph. At what point will John pass Paul

Answer 1

Let x = time since 7 PM

 

Distance = (Rate)(Time)

 

Paul's distance traveled since 7 PM = 50x

John's distance traveled since 7 PM = 70(x-0.5)

 

John passes Paul when the distances are equal:

 

50x = 70(x-0.5)

 

50x = 70x - 35

 

-20x = -35

 

      x = 1.75 hours

 

John passes Paul 1.75 hours after 7 PM  (at 8:45 PM).