# How could the driver waste time? [closed]

A road passes through two small villages, A and B, as shown in the map below.

A truck traveled on that road eastwards at a constant speed of 30 miles per hour and passed through village A at 5pm, but arrived in village B at 6:15pm. The driver never stopped, changed the speed, or turned the steering wheel. The speedometer always showed 30 miles per hour and worked correctly. The map is accurate.

How is this possible?

• Are villages A and B in the vicinity of at least one black hole, and is the observer distant from those villages in some sense? Apr 14, 2020 at 19:55
• By carrying a very large load, relativistically Apr 14, 2020 at 21:40
• If you make the time 6:04pm it wouldn't change the premise of the puzzle any, but the answer would be more believable/not cause so much protest, with reference to the current world record for the factor on which the answer depends... Apr 15, 2020 at 7:37

Maybe Village B is near the

southwestern border of Nepal

so the trip from Village A

crosses the India-Nepal border eastward, so you have to turn your clock forward by 15 minutes because of the time zones: India is at GMT+5:30, Nepal is at GMT+5:45.

• That is clever. I did not know this
– DrD
Apr 13, 2020 at 15:01
• That moment when an answer is more right than the "right" answer :)
– Rubio
Apr 13, 2020 at 16:15
• Likewise, I didn't realize anybody had a time zone off by 15 minutes. Apr 14, 2020 at 0:09
• @LorenPechtel Time zones are a nightmare. Watch youtube.com/watch?v=-5wpm-gesOY Apr 14, 2020 at 6:36
• @vsz Indian and Nepali nationals do not need passports or visas to enter each other's countries. The border is unfenced, and "unofficial" border crossings are not uncommon. So... Yes? Apr 14, 2020 at 14:14

Maybe there was

a large hill (or valley) between A and B, adding some vertical distance that the driver had to travel?

• Yes, you cracked the puzzle :) Here is an illustration of the answer: live.staticflickr.com/3314/3618540648_fecfab2936_b.jpg Apr 13, 2020 at 11:02
• In order to increase the traveled distance by ratio 5:4, the road would need to have a constant 3:4 slope (or a 75% gradient), which is utterly impossible for any car, uphill or down. The steepest streets on the planet don't exceed 45%.
– Bass
Apr 13, 2020 at 14:41
• @Bass, wow, TIL that 10 degrees is already steep. I always assumed that cars can travel at least 30 degrees slope (57%). Maybe we can reason that the road is U-shaped, with the car using the downward momentum to climb upwards on the other side. Apr 14, 2020 at 7:10
• @Bass Most offroad cars are OK with 30deg / 75% slope both uphill and downhill (or even a bit more) from factory. The driver being brave enough or adequate enough is another matter. Apr 14, 2020 at 9:45
• @TCooper The premise is that the person is traveling via a standard vehicle, so yes, it affects the puzzle. Apr 15, 2020 at 19:22

Another possibility:

The truck has had its tires replaced by smaller-diameter low-profile tires, and has not had its speedometer re-calibrated to the smaller wheels, so while it registers 30 mph, it is actually driving considerably slower.

This works because a typical speedometer gauges your speed based on the rotation of the wheel axis. Since smaller wheels require more rotation to produce the same amount of horizontal travel, this would result in it giving you faster-than-accurate readings.

• I wouldn't consider that as a correctly working speedometer, as specified in the question. Apr 14, 2020 at 14:55
• @DidierL The speedometer is functioning perfectly correctly. It just doesn't know that the wheel diameter is not what it's rated for. If you swapped the wheels back to the correct rated size, it would again display accurate readings, so there's nothing wrong with the instrument itself - it is performing exactly as designed. It's only the wheels that are incorrect. Apr 14, 2020 at 15:10
• Well, the speedometer is clearly not calibrated correctly… after that, it's matter of interpretation, I guess :) Apr 14, 2020 at 15:20
• +1. Still more plausible than crossing from India to Nepal without steering the wheel for 60 miles nor stopping at the border.
– Pere
Apr 14, 2020 at 17:49
• +1 And more plausible than a vehicle traveling up and down the slope required for this puzzle. Apr 15, 2020 at 6:24

A treadmill. A very, very big treadmill.

• I was thinking just a treadmill on the back of a large flatbed truck, with the other (presumably smaller) truck on top of it. Apr 14, 2020 at 13:50
• That's what I was going to say! :)
– Almo
Apr 14, 2020 at 20:56
• It could also be a small treadmill (well, one that can fit a truck) going near 30 mph that makes the truck waste 15 minutes in a very short distance.
– JiK
Apr 16, 2020 at 14:52
• If a truck fits on it, it's a big treadmill. :D Apr 16, 2020 at 15:01

The villages are 50 miles north of the south pole, and the road is on a circle of radius 50 miles centered at the south pole. The 10 mile measurement line is placed 10 miles south of this circle on the 40 miles radius circle. Due to the map projection, the distance between the villages looks like it's 30 miles, while it is actually 1.25 * 30 miles, which takes 75 minutes.

Maybe there was snow or mud and lots of head wind that caused the wheels to slip. The speedometer indicated 30 mph but the real speed was less :)

The total distance travelled must be 37.5 miles. If the road follows a sine wave, which would seem to be the most efficient creation of 'hills'. The Arclength becomes 37.5, dx is 30. Varying the amplitude and frequency of the sine wave (or cos) can give various correct values.

• Hi, welcome to puzzling SE! To me, the 'efficient' road sound like a super steep one, it doesn't necessary need to be a sine wave. Apr 14, 2020 at 6:52
• A sine wave has flat portions, so the steepest parts would get even steeper, but even if you used a triangle wave shape (constant slope, alternating between uphill and down) to minimise the maximum steepness, you'd still need a completely undrivable 75% gradient for the entire trip. For comparison, a FIS approved world ski championship slalom course "may exceed approximately 52% only in very short parts of the course".
– Bass
Apr 14, 2020 at 16:59
• I don't know where 75 degrees comes from, if we create a triangle who's adjacent is 30, Hypotenuse is 37.5. that gives us an incremental angle of 36.87 degrees assuming we always go up! If we go up AND down in equal amounts then that halves albeit producing a triangular wave. A sine was chosen to minimise the rate of change of slope. Apr 21, 2020 at 9:09
• @WayneBeckett no one said 75 degrees, they said 75%.. which is indeed 36.87 degrees. Sounds like 6 of one and half a dozen of the other to me! :) Aug 8, 2020 at 4:00

The truck is a Road-Transferable Locomotive, using its Rail-mode to follow a tramline along the road.

This allows its path to turn off-road and travel additional distance, talking more time to complete at the same speed, without the driver turning the steering wheel.

or this:

The question states that the driver does not turn the steering wheel but does not stipulate what the initial position of it was. If the steering wheel is offset then the truck would follow an arc to arrive at village B. The length of this arc could easily add the required additional 7.5 miles to the journey. Assuming of course that the road also follows that arc - only slightly less likely than the road following a dead straight path.

• It could also be a self-driving truck, which would allow the road to have any number of curves in it, which the truck is smart enough to follow. (This would also explain the constant speed, cruise control is pretty good at that.) Although the statement "The map is accurate" kind of defeats either of these options. Apr 15, 2020 at 15:00

Maybe:

The question says that the truck is traveling through village A. So, the discrepancy in the time taken is caused by the truck being in village A at 5:00 PM. So before it can begin its journey to village B it has to first leave village A.

The road is slippery, and while the speedometer is reading 30mph (and functioning correctly) the truck is actually moving slower because of slippage.

The road isn't straight. The reason the driver doesn't turn the steering wheel is that the road is perfectly banked for 30 mph such that at all times the car is moving "straight" forward in the reference frame of the road that it is currently driving over.
Normally we only bank race tracks but it's not impossible to bank other roads.

This map, like many others, uses the Mercator projection. One property of this projection is that distances are increased the closer to the poles one gets. In this particular situation, the villages A and B are located 56 miles north of the south pole. While each square along the line of lattitude marked at the bottom of the map is 5 miles, each square along the line of lattitude connecting the villages is 6.25 miles. So the truck drove 37.5 miles from village A to village B, taking 75 minutes at 30 mph.