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/
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