Patchy and Remi are at the two ends of a hallway 100 meters apart, each running at a steady rate of 5 meters per second toward each other. At the same time, Flan is flying at 10 meters per second away from them in a futile attempt to escape. Flan starts where Remi is and flies until she reaches Patchy, at which point she turns around back toward Remi. In this way, Flan continues back and forth between her two captors. What is the total distance that Flan flies before getting caught?

For anyone interested, here's how to calculate the infinite series.

We see that Flan is flying twice as fast as either Patchy and Remi are running. This means that the when Patchy and Flan first meet, Flan will have traveled twice as far. This is equal to her flying 2/3 the length of the hallway.

Subsequently, Flan will travel 2/3 the distance remaining between Patchy and Remi, which is now 1/3 the length of the hallway. The next distance will be 1/3 of that, and so on, each time with Flan traveling 2/3 of that distance.

The sequence of lengths is then: 100×(2/3) m + 100×(1/3)×(2/3) m + 100×(1/3)x(1/3)×(2/3) m + ⋯

This is a geometric series with rate 1/3 and initial term 100×(2/3), from which we can find the sum as:

>>10880425 Don't bump the thread just to show that you know about the geometric series. This is common knowledge that everyone should obtain at school.

>>10880425 There is no need to calculate the infinite serie. Patchy and Remi travel 50m each at 5m/s, which means they meet 50/5 = 10 seconds later. Flan flies at 10 m/s and thus travels a distance of 10x10 = 100m.

I've always wondered if this could actually work. If a bunch of low-mid Japanese skill level people just agreed on translating a single page each, then agreed on a font, size, etc...

it would probably work quite well if the group translated X pages each, then dumped them into a collection. then everyone in the group would read the whole thing and suggest revisions until they're happy with it (some of them might understand certain phrases on someone else's page).