Distance Word Problem Help

Question

Having problem with setup of a word problem - Two cyclists start at 1:00 PM from opposite ends of a 54-mile race course.  The average rate of speed for the first cyclist is 17mph, and the average rate of speed of the second cyclist is 19mph. At what time will the two cyclist meet?

Answer 1

Let x = time it takes for them to meet

 

When they meet, 

 

distance of first cyclist + distance of second cyclist = 54

 

Distance = (rate)(time)

 

So, 17x + 19x = 54

 

                 36x = 54  so, x = 54/36 hours = 1.5 hours

 

Since they started cycling at 1 PM, they meet at  2:30 PM.