Question 1057376
.
max leaves kansas city and drive east at a speed of 80km/h. one hour late, olivia leaves kansas city traveling in 
the same direction as max but at 96 km/h. assuming neither driver stops for a break, how far from kansas city will 
they be when olivia catches up with max?
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<U>Solution 1</U>


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{{{80/(96-80)}}} = {{{80/16}}} = 5 hours.     (*)

In 5 hours after Olivia's start she will catch up Max.

Olivia will travel 5*96 = 480 km.

<U>Answer</U>.  Olivia will catch up Max at 480 km from Kansas city.

<U>Explanations</U>.  In the formula (*) the numerator "80" is the distance between them when Olivia started her move.

               The denominator 96-80 = 16 km/h is their relative speed.

               The distance between them is decreased 16 km per hour, each hour.

               This "16" is the rate decreasing the distance between the two.
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<U>Solution 2</U>


<pre>
Let "t" be the time (in hours) after Olivia's start moment till the moment she will catches up Max. 

Then the distance she will cover is 96*t.

Max will spent (t+1) hours and will cover the distance 80*(t+1).

These two distances are the same, so you get an equation 

80*(t+1) = 96*t.

Simplify and solve for t:

80t + 80 = 96t,

80 = 96t - 80t,

16t = 80,

t = {{{80/16}}}   (Do you recognize the formula (*) ?)

t = 5.

Thus Olivia will catch up Max in 5 hours and will cover the distance 5*96 = 480 kilometers.

The same answer.
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See the introductory lesson on Travel and Distance problems

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Travel-and-Distance-problems.lesson>Travel and Distance problems</A> 

in this site.