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Hiking Up and Down


Date: 04/24/99 at 22:21:56
From: Kenneth Kwan
Subject: SAT math question

It takes 10 hours to hike from the base of a mountain to the top and 
back down again by the same path. If while hiking a person averages 2 
kilometers per hour going up and 3 kilometers per hour going down, how 
many kilometers is it from the base to the top of the mountain?


Date: 04/26/99 at 14:58:28
From: Doctor Jeff
Subject: Re: SAT math question

Great question, Kenneth!

You are given the total amount of time the person spent hiking, which 
can be split up as follows:

     time-total = 10 hrs = time-up + time-down

You are probably familiar with the formula
  
     distance = rate * time

Since we are dealing with time in the above equation, it is useful to 
rearrange this formula to say

            distance
     time = --------
              rate 

Using this formula, we get

               distance-up                   distance-down
     time-up = -----------  and  time-down = -------------
                 rate-up                       rate-down

Since the distance going up the mountain is equal to the distance 
going down, and since this distance is unknown, we can call it x. We 
also know the rate going up and the rate going down. We can now write

                             x        x
     time-total = 10 hrs = ------ + ------
                           2km/hr   3km/hr

Dividing both sides of the equation by 1 hr and multiplying both 
sides by 1km, we get

                               x     x
     distance-total = 10 km = --- + ---
                               2     3

Solving for x will give you the number of kilometers from the bottom 
to the top (or top to the bottom) of the mountain.

Hope this helped. Good luck with your SATs!

- Doctor Jeff, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Basic Algebra

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