Jon begins jogging at a steady rate of 3 meters per second from the left side of lane 1. Laura also starts
at the left side, but jogs at a rate of 4 meters per second in lane 2. Ellis starts at the right side of lane 4,
100 meters down the track, and runs towards Jon and Laura at the rate of 6 meters per second. After t
seconds, Jon, Laura, and Ellis all lie in a straight line. Compute t.
hello, thanks for the response
i found out that the way to solve the problem was pretty simple
collinear points all have the same slope, so when u solve for the slope of the positions of Jon, Laura, and Ellis, you'll get:
m = 1 / t (slope b/t Jon and Laura)
m = 2 / 100 - 10t (slope b/t Laura and Ellis)
and you set them equal to each other since collinear points have the same slope, and you'll get t = 8.3
With the left and at x=0, after t seconds,
Jon is at 3t
Laura is at 4t
Ellis is at 100-6t
If the lane width is w, then using similar triangles,
(4t-3t)/w = (100-6t - 4t)/2w
2t = 100-6t
t = 12.5
Ah. I see you used 10 m/s for Ellis, whereas I read the problem and used 6 m/s.
To solve this problem, we need to determine the time it takes for Jon, Laura, and Ellis to all lie in a straight line.
Let's consider their positions at time t.
Jon's position at time t is given by:
Distance travelled by Jon = Speed of Jon * Time = 3t
Laura's position at time t is given by:
Distance travelled by Laura = Speed of Laura * Time = 4t
Ellis starts 100 meters down the track at the right side of lane 4 and runs towards Jon and Laura at the rate of 6 meters per second. Therefore, Ellis's position at time t is given by:
Distance travelled by Ellis = Initial distance - Speed of Ellis * Time = 100 - 6t
For all of them to lie in a straight line, their positions should be equal. Therefore, we can set up the following equation:
3t = 4t + 100 - 6t
Simplifying the equation:
3t = 4t - 6t + 100
-3t = 100
Dividing both sides by -3:
t = -100/-3
t = 33.33 seconds (approximately)
Therefore, it will take approximately 33.33 seconds for Jon, Laura, and Ellis to all lie in a straight line.