Question 1187050

A car traveling at 45 mph overtakes a cyclist who, riding at 20 mph, had a 2-hour head start. How far from the starting point does the car overtake the cyclist?
<pre>Let distance from starting point be D
Then time taken for the car and bike to get to the meeting point = {{{matrix(1,3, D/45, and, D/20)}}}, respectively
With the car taking 2 hours less to get to meeting point, we get the following TIME equation: {{{matrix(1,3, D/45, "=", D/20 - 2)}}}
     4D = 9D - 360 ------ Multiplying by LCD, 180
4D - 9D = - 360
   - 5D = - 360
Distance from the starting point, where the bike was overtaken, or {{{highlight_green(matrix(1,6, D, "=", (- 360)/(- 1), "=", highlight(72), miles))}}}</pre>