Question

I really need help with this one question on my math pretests and I have no idea what to do!
The question is:
Mandy begins bicycling west at 30 miles per hour at 11:00 am. If Liz leaves from the same point 20 minutes later bicycling west at 36 miles per hour, when will she catch Mandy?
Pretty please help me, all I need is really just some direction like what to do and if an answer is provided, how you got there. Thanks :)

Answer 1

Liz is going 6 mi/hr faster than Mandy.

By the time she starts, Mandy has gone (1/3)(30) = 10 miles

So, at 6 mi/hr, it will take 10/6 = 1 hr 40 min to catch up with Liz. So, that will be 2 hours after Mandy started, or 1:00 pm.

Or, you can plot both cyclists' positions as a function of t, the time (hours) spent traveling:
Mandy: 30t
Liz: 36(t - 1/3)

30t = 36(t - 1/3)
30t = 36t - 12
6t = 12
t = 2