Question

A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 3.9 m/s. The car is a distance d away. The bear is 23 m behind the tourist and running at 6.0 m/s. The tourist reaches the car safely. What is the maximum possible value for d?

Answer 1

If it takes
`t` seconds to reach the car, then the distance
`d` is
`3.9t`.

The bear's distance from the tourist's starting point is

`6t-23`

For maximum
`d`, we set the equations equal to each other:

`3.9t=6t-23`

`\Rightarrow -2.1t=-23`

`\Rightarrow t=(23)/(2.1)`
so the distance is

`d=3.9((23)/(2.1))\approx42.741\ m`