Hugo backpacks 50 lbs of supplies to the AMC hut near the summit of Mt. Washington every day, up under the sun, up through the rain. On the average day he climbs at the rate of 1.5 miles per hour, but descends at 4.5 miles an hour, making the whole trip in 6 hours. What is the distance from the base camp to the hut?

 
   
 

Hugo must cover the same distance in each direction, therefore the rate going up ● time going up  =  rate going down ● time going down.

With the numbers in: 1.5mph ● Tup = 4.5mph ● Tdown
Simplify by dividing both sides by 1.5: Tup = 3Tdown

Since we know that Tup +Tdown = 6, then Tup = ¾ of 6 = 4.5hrs

Rate ● time = distance; therefore 1.5mph ● 4.5 hrs = 6.75 miles, and the same down.


One of the oldest reasons for mathematics was to make accurate maps. Eratosthenes and Ptolemy did it in ancient times and even today the production of topographic maps from aerial photographs and the fitting of those maps to an integrated global plane are two leading-edge math applications that allow us to navigate the universe around us. No matter how many miles you plan to go.

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