A person is rowing a boat 2 miles from shore, at 5 miles per hour. Immediately on arrival at the shore he takes a taxi 5 miles down the shore, averaging 20 miles per hour. How long will this trip take?

This multi-part journey is a classic example of how to solve for time using the relationship between distance, speed, and time. The key is to remember the fundamental formula: Time = Distance / Speed. To find the total travel time, we must first calculate the duration of each leg of the trip separately. The initial part of the journey is on water, followed by a second part on land, and by calculating the time for each and adding them together, we can determine the total duration of the trip.

For the first segment, the boat is rowed for 2 miles at a speed of 5 miles per hour. Using our formula, we divide the distance (2 miles) by the speed (5 mph), which gives us 2/5 of an hour. For the second segment, the taxi travels for 5 miles at an average speed of 20 miles per hour. This calculation is 5 divided by 20, which results in 5/20 (or 1/4) of an hour. To get the final answer in minutes, we convert these fractions of an hour by multiplying them by 60. The 2/5 of an hour on the water becomes 24 minutes, and the 1/4 of an hour in the taxi becomes 15 minutes.

Summing these two times gives us the total trip duration of 39 minutes. Interestingly, the 5 mph rowing speed is quite brisk for a solo rower. While the idea of for-hire transportation has been around for centuries, with horse-drawn "hackney carriages" first appearing in London in 1605, the first motorized taxi with a meter was introduced in Germany in 1897. This problem combines a timeless mode of transport with a relatively modern one, both governed by the same mathematical principles.