Expert: Sherry Wallin - 9/17/2009

Question
I'm in College Algebra, it's exactly the same thing as Pre-Calculus. There are two questions that I don't understand how to find the answers. I was wondering if you could help me set up the equations and maybe explain why you do it that way. I'm not looking for the answer to the problem. I just need a little help getting started.

The first question has a little geometry in it.
*The perimeter of a triangular plot of land is 2400 ft. The longest side is 200 ft less than twice the shortest. The middle side is 200 ft less than the longest side. Find the lengths of the three sides of the triangular plot.*
The way I set it up was:
2400=(2x-200)-200+2x-200+x

2400(perimeter)=(medium side)+(longest side)+(shortest side)

Everything cancels out in that. So I know it's not right.





The second question is a distance-time-speed based one.
*Scott drives to work in the morning using the toll roads and he averages 60mph. In the afternoon he drives home on free roads and he averages 45mph. It took him 50 minutes longer to make the trip in the afternoon. How Gar does Scott live from work?*
I know t=d/r so d=r*t.
d=60mi*hr

Answer
Amber~
1)  First things first, you need to define your variable. You've used x. Define it to be the length of the shortest side. Now the longest side is 200 ft less than twice the shortest or 2x - 200 and the middle side is 200 ft less than the longest side or 2x - 200 -200. Now sum them up:
x + 2x-200 + 2x -400 = 5x -600 = 2400. 5x = 3000 so x = 600 ft. The shortest side is 600 ft and the middle side is 1200- 400 = 800ft and the longest side is 1200-200 = 1000 ft. What do you mean everything cancels out?
2)  First off d is NOT 60mph, mph is a rate (use rate instead of speed), d is distance and that is what you are looking for. The distance is the same both ways so you want to find a way to represent the distance with the info given. One direction let t =  time so in the morning the distance is 60t and in the afternoon the distance is 45(t+50). Set them equal to each other. 60t = 45(t+50)
15t = 2250 or t = 150 minutes (2.5 hours). But you want distance so 60(2.5) = 150 miles.

Math Prof