SOLUTION: Amy left the zoo and drove south. Nick left three hours later driving 42 km/h faster to catch up to her. After two hours Nick finally caught up. How far did Nick drive?

Two ways.  With or without algebra.  First we'll do it without algebra
and then we'll do it with algebra.

Without algebra:

Since he caught her in 2 hours going 42kph faster, she was 84
km ahead of him when he started chasing her. She had therefore
gone 84km in 3 hours, so she was going 28 kph.  So during the
whole 5 hours she drove 28×5 or 140 km, and that's how far he 
drove too.  So that's the answer. 

With algebra:

Make this chart. 

         distance       rate      time
Amy         
Nick        

Let x = the distance he traveled.  Both traveled the
same distance, so we put x for both his and her distances


         distance       rate      time
Amy         x           
Nick        x          

She traveled for 5 hours and she traveled 5. So fill those
in


         distance       rate      time
Amy         x                      5
Nick        x                      2

Now fill in the rates using 


         distance       rate      time
Amy         x           x/5        5
Nick        x           x/2        2

The equation comes from:



 =  + 42 

Solve that and get x = 140km

Edwin