I need help with this word problem please!

Question

Nicole left the hospital and drove toward her cabin on the lake.  Ryan left one hour later driving 16 km/h faster in an effort to catch up to her. After four hours Ryan finally caught up. What was Nicole's average speed?

Answer 1

N = Nicole's average speed in km/h

R = Ryan's average speed in km/h

a = 1 * N = N km = distance Nicole traveled after 1 hour

 

The total distance Ryan drives when he catches Nicole is:

4(N + 16) and that equals the total distance Nicole has driven when Ryan catches her:

 

a + 4N = N + 4N = 5N

so,

4(N + 16) = 5N

4N + 64 = 5N

64 = N (Nicole's average speed in km/h)