Here's my question. Please walk me through it so I can fully understand it.
Jon begins jogging at a steady 3 meters/sec down the middle of Lane #1 of a public track. Laaura 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 headed toward 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.
Any help is appreciated, even if you can only solve one part. Thank you!
I answered this yesterday. Did you read my answer?
No, I never got to. I'm sorry about that! I guess it would be a few pages back, then?
Thank you very much! I'll respond again or post another message if I have any other problems with your response.
My previous answer can be found at at
http://www.jiskha.com/display.cgi?id=1231284425
Thank you so much! You were a great help.
a. To solve this problem, we can start by determining the distance each runner has covered after t seconds.
Let's start with Jon who is running at a steady speed of 3 meters/sec. The distance Jon covers after t seconds can be calculated using the formula: distance = speed × time. In this case, Jon's distance is given by 3t.
Next, we consider Laura, who is running at a speed of 4 meters/sec. Similar to Jon, Laura's distance can be calculated as 4t.
Finally, there is Ellis, who starts at 100 meters down the track and is headed towards Jon and Laura. Ellis is running at 6 meters/sec. Since he is moving towards Jon and Laura, we subtract his distance from the initial distance of 100 meters. Therefore, Ellis' distance can be calculated as 100 - 6t.
b. When considering the location of each runner as a point on a graph, we can use the x-coordinate to represent time (t) and the y-coordinate to represent the distance covered.
For example, we can use (t, 3t) to represent Jon's position, (t, 4t) to represent Laura's position, and (t, 100 - 6t) to represent Ellis' position.
c. To tell if three points are on a line, we can check if the slope of the line connecting any two points is the same as the slope connecting the third point.
In this case, if Jon, Laura, and Ellis lie in a straight line, then the slope between Jon and Laura should be the same as the slope between Jon and Ellis, as well as the slope between Laura and Ellis.
To find the slope between two points (x1, y1) and (x2, y2), we can use the formula: slope = (y2 - y1) / (x2 - x1).
By calculating the slopes between each pair of points, if the slopes are all the same, then we can conclude that the runners lie in a straight line.
To solve the problem, substitute the expressions for the distances of each runner into the slope formula and equate the slopes to each other. By solving this equation, you will find the value of t, which represents the number of seconds the runners will lie in a straight line.
I hope this explanation helps you understand the problem better. Let me know if you have any further questions!