Applications of Systems of Linear Equations

Algebra
Tutor: None Selected Time limit: 1 Day

Braving blizzard conditions on the planet Hoth, Luke Skywalker sets out in his snow speeder for a rebel base 4800 mi away. He travels into a steady head wind and makes the trip in 3 hr. Returning, he finds that the trip back, now with a tailwind, takes only 2 hr. Find the rate of Luke's snow speeder and the speed of the wind.

May 20th, 2015

Denote the speed of the speeder as x and the speed of the wind as y. Then

4800 = (x - y)*3 = 3x - 3y,
4800 = (x + y)*2 = 2x + 2y.

It is a system of linear equation, solve it by substitution:

from the second equation x = (4800 - 2y)/2 = 2400 - y, substitute to the first:
4800 = 3*(2400 - y) - 3y = 3*2400 - 6y,
6y = 2400, y = 400 (miles/hour),
so x = 2400 - y = 2000 (miles/hour).

Answer: rate of Luke's snow speeder is 2000miles/hour and the speed of the wind is 400miles/hour.

May 20th, 2015

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