Here is another train puzzle, this time from J. A. H. Hunter’s Entertaining Mathematical Teasers:
“Mike had made the [train] trip many times. ‘That’s the morning express from Tulla we’re passing,’ he said. ‘It left Tulla one hour after we pulled out from Brent, but we’re just 25% faster.’ ‘That’s right, and we’re also passing Cove, two-thirds the distance between Brent and Tulla,’ Martin agreed. ‘So we’re both right on schedule.’ Obviously a couple of train buffs! Assuming constant speeds and no stops, how long would it be before they reached Tulla?”
See the Train Buffs
This is another train puzzle by H. E. Dudeney. This one has some hairy arithmetic.
“Two trains, A and B, leave Pickleminster for Quickville at the same time as two trains, C and D, leave Quickville for Pickleminster. A passes C 120 miles from Pickleminster and D 140 miles from Pickleminster. B passes C 126 miles from Quickville and D half way between Pickleminster and Quickville. Now, what is the distance from Pickleminster to Quickville? Every train runs uniformly at an ordinary rate.”
See Trains – Pickleminster to Quickville
Yet another train problem from H. E. Dudeney.
“We were going by train from Anglechester to Clinkerton, and an hour after starting an accident happened to the engine. We had to continue the journey at three-fifths of the former speed. It made us two hours late at Clinkerton, and the driver said that if only the accident had happened fifty miles farther on the train would have arrived forty minutes sooner. Can you tell from that statement just how far it is from Anglechester to Clinkerton?”
See the Damaged Engine.
This is another train puzzle from H. E. Dudeney, which is fairly straight-forward.
“I put this little question to a stationmaster, and his correct answer was so prompt that I am convinced there is no necessity to seek talented railway officials in America or elsewhere. Two trains start at the same time, one from London to Liverpool, the other from Liverpool to London. If they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?”
See Two Trains – London to Liverpool
This is one of H. E. Dudeney’s train puzzles.
“Two railway trains, one four hundred feet long and the other two hundred feet long, ran on parallel rails. It was found that when they went in opposite directions they passed each other in five seconds, but when they ran in the same direction the faster train would pass the other in fifteen seconds. A curious passenger worked out from these facts the rate per hour at which each train ran. Can the reader discover the correct answer? Of course, each train ran with a uniform velocity.”
See Two Trains – Passing in the Night.
Here is another Presh Talwalkar problem that seems unsolvable at first glance.
“Every day, a train passes a train station along a straight line track, and the train moves at a constant speed. Two friends, A and B, want to determine how long the train is. Lacking proper equipment, they devise the following method. They first synchronize their walking. Both A and B walk at the same constant speed, and each step they take is the same length. One day they line up back to back at the train station. When the front of the train reaches them, they both start walking in opposite directions. Each person stops exactly as the back of the train passes by. If person A takes 30 steps, and person B takes 45 steps, how long is the train, in terms of steps?”
See the Train Length Puzzle.