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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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Solution 1
= = 5 hours. (*)
In 5 hours after Olivia's start she will catch up Max.
Olivia will travel 5*96 = 480 km.
Answer. Olivia will catch up Max at 480 km from Kansas city.
Explanations. 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.
Solution 2
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 = (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.
See the introductory lesson on Travel and Distance problems
- Travel and Distance problems
in this site.