The following problem from Five Hundred Mathematical Challenges was a challenge indeed, even though it appeared to be a standard travel puzzle.
“Problem 118. Andy leaves at noon and drives at constant speed back and forth from town A to town B. Bob also leaves at noon, driving at 40 km per hour back and forth from town B to town A on the same highway as Andy. Andy arrives at town B twenty minutes after first passing Bob, whereas Bob arrives at town A forty-five minutes after first passing Andy. At what time do Any and Bob pass each other for the nth time?”
See the Perpetual Meetings Problem
This is another intriguing problem from Presh Talwalkar.
“A car travels 75 miles per hour (mph) downhill, 60 mph on flat roads, and 50 mph uphill. It takes 3 hours to go from town A to B, and it takes 3 hours and 30 minutes for return journey by the same route. What is the distance in miles between towns A and B?”
See the Impossible Car Riddle
This turns out to be a fairly challenging driving problem from Longley-Cook.
“Mileage on the Thru-State Turnpike is measured from the Eastern terminal. Driver A enters the turnpike at the Centerville entrance, which is at the 65-mile marker, and drives east. After he has traveled 5 miles and is at the 60-mile marker, he overtakes a man operating a white-line painting machine who is traveling east at 5 miles per hour. At the 35-mile marker he passes his friend B, whose distinctive car he happens to spot, driving west. The time he notes is 12:20 p.m. At the 25-mile marker he passes a grass cutter traveling west at 10 miles per hour. A later learns that B overtook the grass cutter at the 21-mile marker and passed the white-line painter at the 56-mile marker. Assuming A, B, the painter and the grass cutter all travel at constant speeds, at what time did A enter the turnpike?”
See Turnpike Driving.
This is another puzzle from the Futility Closet that was originally from Henry Dudeney’s Canterbury Puzzles.
“A country baker sent off his boy with a message to the butcher in the next village, and at the same time the butcher sent his boy to the baker. One ran faster than the other, and they were seen to pass at a spot 720 yards from the baker’s shop. Each stopped ten minutes at his destination and then started on the return journey, when it was found that they passed each other at a spot 400 yards from the butcher’s. How far apart are the two tradesmen’s shops? Of course each boy went at a uniform pace throughout.”
See the Two Errand Boys.