Imagine that there is a circular track given by the equation x2+y2=2102500, where both x and y are measured in units of feet. At time t=0, Robin is at point (1450,0) and Shannon is at point (−170,1440). Both are running counterclockwise, with Shannon running at 2.3 feet per second and Robin running at 3.6 feet per second.
Answer is not: 3373.01192
Robin runs until he catches Shannon. How long does that take?
At what point do Robin and Shannon meet?
To find the time it takes for Robin to catch up to Shannon, we can set up an equation based on their motion.
Let's assign variables to their positions at any given time: Robin's position is given by (x1, y1) and Shannon's position is given by (x2, y2).
Since Shannon is running counterclockwise, their positions can be modeled as follows:
x1 = 1450 + 3.6t (Robin's x-coordinate at time t)
y1 = 0 (Robin's y-coordinate, which remains constant)
x2 = -170 + 2.3t (Shannon's x-coordinate at time t)
y2 = 1440 (Shannon's y-coordinate, which remains constant)
We want to find the time when Robin catches up to Shannon, which means their positions will be the same at that time. So, we can set up the following equation:
(x1 - x2)^2 + (y1 - y2)^2 = 0
Substituting the given expressions:
(1450 + 3.6t - (-170 + 2.3t))^2 + (0 - 1440)^2 = 0
Simplifying the equation:
(1620 + 1.3t)^2 + 2073600 = 0
Now, solving this equation for t can provide us with the answer. However, it seems that the answer you provided (3373.01192) does not satisfy this equation. Please double-check your answer or provide more information if needed.
Reiny did this already at
http://www.jiskha.com/display.cgi?id=1461201861