Darren New <dne### [at] sanrrcom> wrote:
> Jim Henderson wrote:
> > On Wed, 20 Jan 2010 08:11:28 -0800, Darren New wrote:
> > 
> >> Warp wrote:
> >>>   I have hard time parsing that question.
> >> It *is* messed up. The usual question is something like
> >>
> >> You have a race two miles long. For the first mile, one car goes 60MPH
> >> and the other goes 30MPH. How fast does the other car have to go to
> >> finish the race at the same time as the one going 60MPH?
> > 
> > Even then it doesn't parse correctly, because they've given you the 
> > speeds for both cars - so asking how fast the slower car should go 
> > doesn't make sense, because you've been told how fast it is going.

> The race is two miles long. The slow car goes at a speed for one mile. 
> What's the speed in the second mile?

  I understood it to mean "when the faster car hits the one mile mark,
how fast should the slower car go from that point forward in order to
catch up and get to the finish line at the same time as the faster car"
(which is an interesting question).

  However, if it really meant "when the *slower* car hits the one mile
mark, how fast must it go from that point forward to catch up" it becomes
a trick question (because the faster car has already reached the finish
line by that point).

> Anyway, that's an easy question to answer. A slightly better version is this:

> You want to average 60MPH over two minutes. You go 30MPH for the first mile. 
> How fast do you have to go to average 60MPH for two minues?

> Second alternate question: you want to average 60 MPH. You drive 10 miles at 
> 30MPH. How many miles do you need to drive at 90MPH to average 60MPH?

  I like this version of two things going at different speeds more (I don't
remember the *exact* setup, so I'll just invent the numbers):

  A man and a dog are walking home, which is at a distance of 1 mile.
The man walks at 3 mph. The dog start running at 10 mph towards home.
When it reaches it, it turns around and runs back to the man (keeping
the 10 mph velocity at all times), then turns around and runs to home,
and so on, until the man reaches home. What's the total distance that
the dog ran?

  The problem sounds like you would need to calculate an infinite sum,
but there's actually a much simpler solution.

  (There's also an anecdote of this problem having been given to some
mathematician (don't remember name), and him giving the answer almost
immediately. The person who posed the problem then remarked that "ah,
you figured out pretty fast that you don't need an infinite sum to get
the answer, but that there's a much simpler way", to which the mathematician
responded "what? I *did* use an infinite sum".)

-- 
                                                          - Warp

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