I've been taking a practice accuplacer test (this one), after checking my answers I found that I got the following question wrong:
2. Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking? However I can't for the life of me figure out what I did wrong. The answer is B but I got E.
A. 2 hours
B. 4 ½ hours
C. 5 ¾ hours
D. 6 hours
E. 7 ½ hours
I modelled the first cyclist with the equation y = 6x , and the second with the equation y = 10x - 30. I derived these from a graph I drew, time on the x axis and distance from the trail head on the y axis using hours and miles as units. I asked my brother and he used the equations y = 6x + 18 (for the first cyclist), and y = 10x (for the second). Those yielded the correct answer, but both of us agreed that my equations adequately represented the situation too. We concluded that my equation didn't work because it assumes that the second cyclist bicycled 30 miles to the trail whereas the first started out at the trail head, and so the second was tired by the time he got there. But that doesn't fix anything. Where did I go wrong?