# Speeding car

1. Feb 25, 2005

### vikasj007

a car is travelling at a uniform speed. the driver sees a milestone showing a two digit number. after travelling for one hour the driver sees another milestone with the same digits reversed. after another hour he comes across yet another yet another milestone containing the same two digits.

what is the average speed of the driver?

2. Feb 25, 2005

### Icebreaker

The driver's amnesiac. His speed is zero.

3. Feb 25, 2005

### vikasj007

come on icebreaker, you can do better than that.

4. Feb 25, 2005

### nnnnnnnn

45 unfortunately I found out by accident just trying to set up an equation...

5. Feb 25, 2005

### RandallB

I won't give away the answer, but after passing the first mile marker by 33 miles you find a pair of digits that also reappear one hour from there.
Now of course those two digits when added together sum to the same number. But one hour after that is a three digit maker that also sums those digits to the same number. As do the digits in the other three sets of markers.

I'm sure it's all relative to closeness to multiples of 3.

RB

Last edited: Feb 25, 2005
6. Feb 25, 2005

### nnnnnnnn

RB how did you figure that out?

7. Feb 26, 2005

### vikasj007

now that we have the answer, can somebody(other than nnnnnnn) tell the distance written on milestones.

8. Feb 26, 2005

### brout

Just find this out ... with a bit of luck :) ....
16 / 61 / 106 => 45mph

9. Feb 26, 2005

### Bartholomew

The milestones were 122100, 122105, and 122110. His speed was 5 mph.

10. Feb 26, 2005

### DaveC426913

A clever try Bart, but it does say the driver sees "...a milestone showing a two digit number".

Two digits out of a six digit number is not a "two digit number".

11. Feb 26, 2005

### Bartholomew

Okay, 11, 111, and 211; speed 100 mph.

12. Feb 26, 2005

### Bartholomew

Or, actually, almost any speed would work. The driver travels at a constant speed, not necessarily constant velocity; mile markers on one road don't have to have anything to do with mile markers on another road, and the driver can switch roads.

13. Feb 26, 2005

### Bartholomew

Or assuming he keeps to the same road... markers say .18, 81, and 161.82, for a speed of 80.82 mph.

14. Feb 26, 2005

### Abstruce

The answer should be 100 MPH however the number would climb to over two digits you are only referencing the last two digits.

This first milestone is 00 traveling at one hour at 100 miles per hour the second milestone is 100 another hour later at 100 miles per hour the milestone reeds 200 miles.

Or the correct answer is traveling at a rate of 150 miles per hour.

one hour later at 150 MPH

one hour later at 150 HPH

Last edited: Feb 26, 2005
15. Feb 26, 2005

### RandallB

You can always tell, no matter how large a number is, if it is divisible by 3 or 9; by adding continuing to add the individual numbers together. Any remainder after doing the sums is how far off of an even multiple of 3. (Or 9 if that’s what your working with)

Think of viewing it as a pattern between the base 3 numbering system to interface with our base 10 system.

Which is why the original problem working from the mile marker 16 (1 over a multiple of 3): In a four digit mode does not work from mile marker 1016 (2 over a multiple of 3) or 2016 (an even multiple of 3 {and 9})
But does work from 3016 (Also 1 over a multiple of 3).
But you don't find many 4 digit mile markers.

I'd put your running into the solution “by accident just trying to set up an equation” on some internal instinct you didn’t know you were using.

Good puzzle.