SOLUTION: The distance between Majorie and the dude ranch was (4times the square root of 34) miles straight across a rattlesnake-infested canyon. Instead of crossing the canyon, she hiked d

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Question 155368This question is from textbook College Algebra
: The distance between Majorie and the dude ranch was (4times the square root of 34) miles straight across a rattlesnake-infested canyon. Instead of crossing the canyon, she hiked due north for a long time and then hiked due east for the shorter leg of the journey to the ranch. If she averaged 4mph and it took her 8 hr to get to the ranch, how far did she hike in a northernly direction?
( they show a right triangle and i have the answer but i dont know how to set up the formula.the answer is 20 miles)( they show the hypontenuse as 4xthe sq rt of 34) and the loner leg is going north and the shorter leg is going east) This question is from textbook College Algebra

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The distance between Marjorie and the dude ranch was (4times the square root of 34) miles straight across a rattlesnake-infested canyon. Instead of crossing the canyon, she hiked due north for a long time and then hiked due east for the shorter leg of the journey to the ranch. If she averaged 4mph and it took her 8 hr to get to the ranch, how far did she hike in a northernly direction?
( they show a right triangle and i have the answer but i don't know how to set up the formula.the answer is 20 miles)( they show the hypotenuse as 4xthe sq rt of 34) and the loner leg is going north and the shorter leg is going east)
:
They give the travel time and the speed, find the total distance
8 * 4 = 32 mi total
:
Let x = the northern leg
then
(32-x) = the shorter eastbound leg
:
The famous right triangle formula:
x^2 + (32-x)^2 = (4sqrt%2834%29)^2
;
x^2 + (1024 - 64x + x^2) = 16(34)
:
x^2 + x^2 - 64x + 1024 = 544
:
2x^2 - 64x + 1024 = 544
:
2x^2 - 64x + 1024 - 544 = 0
:
2x^2 - 64x + 480 = 0
Simplify, divide by 2
x^2 - 32x + 240
Factors to:
(x-12)(x-20) = 0
:
x = 20 mi is the longer leg distance
:
:
Check solution on calc:
Entersqrt%2820%5E2+%2B+12%5E2%29 = 23.3238 which is 4sqrt%2832%29