Question

A tourist being chased by an angry bear is running in a straight line toward his car at a speed of 4.2 m/s. The car is a distance d away. The bear is 30 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

Time taken for the tourist to reach the car is
\[t=\frac{distance}{speed}=\frac{d}{4.2}\ ........(1)\]
Time taken for the tourist to reach the car is
\[t=\frac{distance}{speed}=\frac{d+30}{6}\ ......(2)\]
If the tourist and the bear reach the car at the same time, we can equate (1) and (2) giving:
\[\frac{d}{4.2}=\frac{d+30}{6}\ ...........(3)\]
Cross multiplying and simplifying equation (3) gives
1.8d = 126
which leads to a maximum possible value for d of:
\[d=\frac{126}{1.8}=you\ can\ calculate\]