A car is travelling at a uniform speed.
The driver sees a milestone showing a 2-digit number. After travelling for an hour the driver sees another milestone with the same digits in reverse order. After another hour the driver sees another milestone containing the same two digits as in the first one but the two digits separated by a zero(0).

What is the speed of the car?

You know, I'm no big math stud, but I saw from teh titles that fwaff had come up with a "no btute force colution" I was going to read it as those solutions are so muchmor elegant than the old "i punched it into a spread sheet and here's what came out answers but then I decided to see if I could do it. Here is what I came up with, I hope its as good as whatever fwaff had:

first define the first milemarker number as AB where A and B are just digits with no mathmatical operations intended bejond the old ones place, tens place thing.

Since the car is going a uniform speed and the first to milesones mentioned are two digit numbers the car must be travelling less than 100 miles per hour. therefore the difference between the second two milestones must be less than 100 therefore the third milestone number (defined in this case a A0B) must be less than 200 so A must equal 1.

this being the case we can write the mubmers of the three stones thusly:
"1B"
"B1"
"10B"

(with everything still representing digits and no additional operations implied)

This means however we can write the numbers mathematically as follows
"1B" = 10+B
"B1" = (10*B)+1
"10B" = 100 + B

since we know the speed was constant the difference between teh first two must be the same as the difference between the second two
therefore
[(10*B)+1] - (B+10) = (100+B) - [(10*B)+1]
through my remaining HS Algebra I therfore concluded that B = 6

this means the three stones read 16, 61 and 106
The car was going 45mph

not elegant, I admit and it probably would have been more studly to set it up with both A and B as variables in math equations and hash it out from there but I like my way anyway.

Posted by FatBoy on 2003-10-03 10:12:57