➡ The Problem

Two ships leave the port of San Diego, both sailing for the distant shores of Japan. Each ship plans to travel the same route, spending a two-week stopover in Tokyo before returning to California. The first ship churns through the sea at 35 miles per hour throughout the entire journey. The second ship moves slower, at just 30 mph. After two weeks in Tokyo, the captain of the second ship decides to run at a faster pace, moving at 40 mph for the entire return trip. Which ship arrives in San Diego first?

➡ The Solution

The thing I like most about this riddle is that it doesn’t seem like a riddle at all. Our knowledge of averages make it seem like both ships travel the same speed overall, so they obviously arrive at port at the same time. However, even looking at a simplified version of this puzzle shows the mistake in this logic.

Imagine these ships are only traveling 120 miles. The blue ship moves 35 mph. The red ship moves at 30 mph until it hits half the total distance, then starts moving at 40 mph.

ship diagram
Richard Malena

Consider where the ships are after three hours and how long it will take them to cover the remaining miles to the finish line. The red ship is easy. At a speed of 40 mph, it takes another half hour to travel the last 20 miles. The blue ship is only 15 miles away. At a speed of 35 mph, it crosses the finish line in just a little bit less than half an hour—25.7 minutes. Blue wins!

If this seems counter-intuitive, I agree. But here’s the thing: If I drive at 30 mph for 30 minutes and then step it up to 40 mph for another 30 minutes, then our intuition does work. I’m driving at an average speed of 35 mph. But that situation only compares speed and time. In this riddle, the problem is that the halfway point is defined by distance.

Let’s run the general scenario with a classic physics equation, distance = rate x time. Or, in this case, time = distance / rate. We’ll set d equal to a constant distance of one ocean crossing, or half the voyage, and try to compare the amount of time each ship is on the water.

math equation
Richard Malena

The specific numbers aren’t as important as the comparison between them. Since d is a constant, we can now see that the blue ship makes the journey in a shorter amount of time and reaches San Diego first. It’s not quite a tortoise and the hare story, but steady still wins the race!

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