Two Trains Fly Puzzle Answer: 60 Miles [Solved]

The two trains fly puzzle answer is 60 miles. Two trains start 60 miles apart and race toward each other at 30 miles per hour each. A fly shuttles between them at 60 miles per hour. The trains meet after one hour, so the fly flies for one hour. One hour at 60 miles per hour is 60 miles. Below: the one-step answer, the endless series that traps most candidates, and the follow-up questions interviewers ask next.

The two trains fly puzzle is a classic from the interview circuit. It carries a famous story: John von Neumann is said to have summed the infinite series in seconds, then smiled at the shortcut. The question looks like hard work, and the answer is one line of arithmetic. That gap is why interviewers keep asking it.

The Two Trains Fly Puzzle, Stated Plainly

Two trains are on the same track, 60 miles apart, heading toward each other. Each train travels at 30 miles per hour. The trains start moving. At the same moment, a fly takes off from the front of the first train. It flies toward the second train at 60 miles per hour. When the fly reaches the second train, it turns around instantly and flies back toward the first train. It keeps flying back and forth between the two trains until they meet. How far does the fly travel in total before the trains meet?

Four facts are worth fixing before you start. First, the fly flies at a constant speed of 60 miles per hour. Second, it turns around instantly, so no time is lost at either end. Third, the fly keeps flying until the exact moment the trains meet. Fourth, the question asks for total distance, not total time or the number of trips.

The Two Trains Fly Puzzle Answer in One Step

Start with the trains, not the fly. The two trains are 60 miles apart. They close the gap at a combined speed of 30 plus 30, which is 60 miles per hour. So they meet after 60 divided by 60, which is exactly one hour.

Now look at the fly. The fly is in the air for that whole hour, from start to meeting. It flies at a constant 60 miles per hour for one hour. So it covers 60 times 1, which is 60 miles.

That is the whole solution: work out how long the fly flies, then multiply by its speed. The fly makes countless trips back and forth. The answer never needs any of them. The interviewer is watching for the moment you stop counting trips and start counting time.

Why the Short Road Works

The trick is a change of question. “How far does the fly travel?” sounds like a distance problem, so most candidates start adding up distances. But distance is speed times time, and the time is easy. The fly flies for exactly as long as the trains take to meet. Once you see that, the fly becomes a clock, not a traveller. The arithmetic is one multiplication.

The Series Trap: Why Candidates Add Legs Forever

The natural first move is to work out each leg and add them up. That road leads to the same answer, but it is long. Most candidates run out of time or make an arithmetic slip before they get there. It is still worth seeing: it proves the short answer is right.

The Two Trains Fly Puzzle, Leg by Leg

Leg 1: the fly leaves the first train and flies toward the second. The two are closing at 60 plus 30, which is 90 miles per hour. They start 60 miles apart. So the first leg takes 60 divided by 90, which is two thirds of an hour. In that time the fly covers 40 miles. Meanwhile each train has moved 20 miles, so the gap is now 20 miles.

Leg 2: the fly turns and flies back. The gap is 20 miles. The closing speed is still 90 miles per hour, so this leg takes 20 divided by 90, which is two ninths of an hour. The fly covers 13.33 miles. Each train moves 6.67 miles. The gap is now 6.67 miles.

Leg 3 covers about 4.44 miles, and leg 4 about 1.48 miles, as the gap falls to 2.22 miles, then 0.74 miles.

Leg	Gap at the start	Fly distance	Running total
1	60 miles	40 miles	40 miles
2	20 miles	13.33 miles	53.33 miles
3	6.67 miles	4.44 miles	57.78 miles
4	2.22 miles	1.48 miles	59.26 miles
And so on	Keeps shrinking	Keeps shrinking	60 miles

The Infinite Sum

Each leg is exactly one third of the leg before it. So 13.33 is one third of 40, and 4.44 is one third of 13.33. So the total is 40 times (1 + 1/3 + 1/9 + …). That infinite sum is 40 times 3/2, which is 60 miles. The series agrees with the one-step answer. It also shows why the series is the wrong tool in an interview. You can spend the whole hour adding legs and still be short of the answer. The time trick finishes the problem in two sentences.

What the Interviewer Is Testing in the Two Trains Fly Puzzle

First, the puzzle tests whether you reframe a problem before you start calculating. The candidates who do well pause and ask what they actually need. The fly total distance is speed times time, and the time comes from the trains. Candidates who start adding legs show they can calculate, but not that they looked for the simpler view.

Second, it tests comfort with infinity. The fly makes an endless number of trips, and the legs get shorter without ever reaching zero. Some candidates freeze at the word endless. The strong answer is that an endless number of shrinking legs still adds up to one finite number. That number is 60 miles.

Third, it tests whether you check your answer by a second route. The best candidates give the one-step answer, then show the first two legs: 40 miles and 13.33 miles. The running total is already past 53 miles and climbing toward 60. That check takes twenty seconds, and it shows the interviewer you test a shortcut before you trust it.

Follow-Up Variations Interviewers Ask Next

Unequal train speeds. Suppose the trains travel at 40 and 20 miles per hour, and they start 120 miles apart. The fly still flies at 90 miles per hour. The trains close at 60 miles per hour, so they meet after 120 divided by 60, which is two hours. The fly flies for two hours at 90 miles per hour. So it covers 180 miles. The method never changes: find the meeting time first, then multiply.

The supersonic bee. In the toughest version, the trains enter a 200-mile tunnel at 100 miles per hour each. A bee flies between them at 1,000 miles per hour. The trains meet after one hour, so the bee covers 1,000 miles. The numbers get dramatic. The method stays the same.

The fly starts from the other train. Nothing changes. The fly still flies for the whole time the trains take to meet, so the answer is the same. A different answer here means the candidate is still adding legs instead of counting time.

Frequently Asked Questions

Does the fly really turn around instantly?

In the puzzle, yes. Real flies need time to turn, and real trains are not points. The puzzle states the turn is instant, so the model is clean. If the interviewer asks what changes with a real fly, the honest answer is that the total would be slightly less. Every turn costs a little time. The idealised answer stays 60 miles.

Where is the two trains fly puzzle asked?

It appears in interview puzzle collections and candidate-shared reports. A Citadel report from 2023 on TechInterview lists it as the bumblebee problem. The question setup is a classic interview brain teaser; the solution and walkthrough above are original.

What should I say first in the interview room?

Say the method before the number. Start with this: “The fly flies for exactly as long as the trains take to meet.” Then give the answer of 60 miles. If you open with “60 miles” and stop, the interviewer cannot tell whether you saw the trick or guessed. The reasoning is the answer.

Try This One Next

If you liked the two trains fly puzzle, try Goldman Sachs 4 Cars Puzzle: Answer 208 Miles [Solved]. It is the same kind of thinking in a different shape. A strict limit, a hidden resource, and one clean idea make the answer fall out. For a second puzzle, try the Bridge and Torch Puzzle Answer: Cross in 17 Minutes [Solved], where the trick is letting the two slowest people cross together.