2440.33 – Susu the Cat

Susu the cat is taking off from the county airport in her trim and elegant Cirrus SR22. She will fly 200 miles to check out a new bird park (don’t ask). Her plane travels at a steady 100 miles an hour. Her route passes over the center of a round lake having diameter 50 miles.

She’s nervous about flying over water, so when she reaches the edge of the lake she turns and flies along its shoreline to the other side, rather than flying straight across. How many minutes does this add to the length of her flight?

Solution

If she flew straight across the lake, her flight would take half an hour, or 30 minutes. By flying halfway around the shore instead, she flies half the circumference of a circle with diameter 50 miles. The full circumference is $50\pi$ , or (using 3.14 for $\pi$ ) 157 miles.

The half-circle that she flies is 78.5 miles. $\text{Time} = \dfrac{\text{distance}}{\text{rate}}$ , so the time for that part of her flight is $\dfrac{78.5 \text{ miles}}{100 \tfrac{\text{miles}}{\text{hr}}} = 0.785 \text{ hours} = 47.1 \text{ minutes}$

This is 17.1 minutes longer than the 30 minutes it would have taken her to fly straight across the lake. The time loss is worth it for her peace of mind.