Question 1195013: There is a 1 m wide road. Two turtles start to crawl down the road from opposite directions towards one another. What is the probability of them not bumping each other if their shell diameter is 11 cm?
turtle_A--->.0
road->|------|-------|
--------|------V-------|
--------|<--1 m---->|
--------|--------^-----|
--------|--------|-----|
-----------------0 <- turtle B
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Below is a diagram we can use to find the answer.
Assume the road, 1m = 100cm wide, has barriers on each side, so that the edges of the turtles can't hang over the edges.
The black lines represent the edges of the road, so they are the limits of where the shells of the turtles can be.
The horizontal axis represents the position of the center of turtle A from one edge of the road; the vertical axis represents the position of the center of turtle B from that edge. Since the shells have a diameter of 11cm, the radius is 5.5cm, so the centers of the turtles can't be within 5.5cm of the edge of the road. The red lines represent the limits of the regions where the centers of the turtles can be.
The blue line ("y=x", or center of turtle A = center of turtle B) represents the two turtles occupying exactly the same position in the road, indicating a head-on collision (with likely little damage, at those speeds!).
The two green lines represent the center of turtle A being 11cm before or after the center of turtle B, representing the two turtles just barely passing each other.
So the regions between the green lines and the edges of the red box represent the cases in which the two turtles pass safely.
The cases in which the two turtles are within the edges of the road are represented by the area of the red box; the cases in which the two turtles pass safely is represented by the areas of the two triangular regions.
The red box is a square with side length 89; the two triangular regions together are equivalent to a square with side length 78.
So the probability that the two turtles pass safely is
 = 0.768 =76.8% to 3 decimal places
ANSWER: 0.768
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