Algebra--help really needed!
posted by Caroleen on .
I'm having some trouble with my algebra homework. Please walk me through the question completely and give me the answer so I can fully understand it if I would ever need to solve a similar problem.
Here's the problem:
#1: Jon begins jogging at a steady 3 meters/sec down the middle of Lane #1 of a public track. Laura starts even with him in the center of Lane #2 but moves at 4 meters/sec. At the instant they begin, Ellis is located 100 meters down the track in Lane #4, and is heading towards them in his lane at 6 meters/sec. After how many seconds will the runners lie in a straight line?
a. Let t be the number of seconds the three have been running. Write expressions for the number of meters each has run after t seconds.
b. Consider the location of each runner as a point on a graph. What quantity might you use as the x-coordinate? What quantity might you use as the y-coordinate?
c. How can you tell if three points are on a line? Use this to solve the problem.
Thanks so much in advance. Any help is appreciated, even if you can only solve one part. Thanks!
The location of J from the starting line is 3 t. The location of L is 4t. The location of E from the starting line is 100 - 6t.
A straight line from J through L intersects the middle of lane 4 at a distance 6t from the starting line. (Remember that lane #3 is empty).
When 6 t = 100 - 6t, the runners are on a straight line.
12 t = 100
t = 8 1/3 seconds
At that time XYjon (lane 1) = 25 m; Ylaura (lane 2)= 33.33 m and Yellis (in lane 4) = 50 m
Make a plot of showing where the runners are in X (lane number) and Y (from starting line) at that time and you will see they fall along a straight line