Question 217867
A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three- hour head start.  How far from the starting point are the two vechicles. 


Let the time that the faster vehicle (motorcycle) takes to get to the meeting point be T


Then the time that the car takes to get to the meeting point is T + 3 since it had a 3-hour head start, and is the slower vehicle


Since Distance = Speed x Time, and in this case the distances are equal, we therefore have: 70T = 40(T + 3)


70T = 40T + 120


30T  =  120


{{{T = 4}}}, which makes the distance that both vehicles traveled, {{{highlight_green(280)}}} miles, calculated as (70 * 4), or (40 * 7).


It also means that the motorcycle took 4 hours to travel 280 miles, and the car took 3 hours more, or 7 hours to travel the same distance.