Question 350273: The distance between Marge and the Dude ranch was 4 square root 34 miles straight across a rattlesnake infested canyon ( hypotenuse). She hiked due north for a longer time then due east for the shorter leg of the journey. If she averaged 4 mph and it took 8 hours to get to the ranch how far did she hike in the northerly direction ?
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! I decided to tackle your question one more and this time I completed it for you.
4 miles/hour x 8 hours = 32 miles total
We are given that the hypotenuse is 4sqrt(34) miles, so she hiked the legs of the triangle.
One leg = a, and the other leg is 32 - a, so we have
a^2 + (32-a)^2 = (4sqrt(34))^2
a^2 + 1024 - 64a + a^2 = 544
2a^2 -64a+480 = 0
a^2 - 32a + 240 = 0
(a-12)(a-20) = 0
a = 12 or a = 20
Since we are given that she traveled North further than South, she hiked 20 miles in the northerly direction.
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