Question 508933
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?
<pre>
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 {{{rate=distance/(time)}}}


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

The equation comes from:

{{{(matrix(2,1,
"Nick's",
rate))=
(matrix(2,1,
"Amy's",
"rate"))+42))}}}

{{{x/2}}} = {{{x/5}}} + 42 

Solve that and get x = 140km

Edwin</pre>