Car Journey

Originally posted by Palynka
I know this puzzle, but don't you need to tell them the total time of each trip?

Nope.

Originally posted by THUDandBLUNDER
When a man drives his car from town A to town B he drives at 72mph downhill and at 56mph uphill.
Using the times taken for both legs of the journey, when he returned home he was able to calculate the distance between the two towns.

How fast does he drive on the flat?

I think there is no flat. Given is his speed going up and going down, stated is that only by this data (and the total time) he could calculate the distance between te two towns. Therefore there really should be no flat in between them.

If i'm wrong I'll take a chance on his speed I guess 80 mph, but there really is no way of telling.

Originally posted by Siebren
I think there is no flat. Given is his speed going up and going down, stated is that only by this data (and the total time) he could calculate the distance between te two towns. Therefore there really should be no flat in between them.

...but there really is no way of telling.

I have already stated that the amount of flat road is non-zero and that it is possible to deduce his speed on it, given his speed off it. 😴

Well the obvious guess would be 63mph

Originally posted by Peakite
Well the obvious guess would be 63mph

Obvious?
Guess?
Hmm...

Well it is the average speed, based on doing the same strech of hill both forwards and backwards. As it is one of only two remotely sensible figures I could think of, that seems far the more likely solution - in that sense the obvious guess.

Is that the mode mean or median average we're talking about?

Mean

Originally posted by THUDandBLUNDER
I have already stated that the amount of flat road is non-zero and that it is possible to deduce his speed on it, given his speed off it. 😴

white flag 🙄

Average speed = Total distance / Total time

Sorry, just thought I'd mention it.

Just some prefacing: t1=time for forward journey, t2=time for return journey, U=uphill distance, D=downhill distance, F=flat distance, vu=uphill velocity, vd=downhill velocity (and something else dirty...hee hee!!!), and vf=flat velocity.

The solution must have something to do with the fact that the man can calculate the distance based on the time taken each way (ie. some combination of t1 and t2 results in a special case which could only be satisfied for a certain vf, which gives you the extra information you need).

t1-t2 is a constant, and setting t1=t2 gives you D=U, but I can't get that working for me. Any help, guys?
😳

The distance can only be calculated from the time taken to do both legs of the trip. As you don't know how much upward or downward slope there is in a particular direction, you cannot come up with an answer for average speed in one direction.

I think Peakite is right and the answer is 63, which is the avg. speed for the round trip on the uphill and downhill portions.

it may not be the only solution to the problem, but we can say this much: if he drives 63 miles per hour on the flat, then he can very simply calculate the distance between A and B with the given information. In fact, i think he wouldn't have to know the individual leg times, only the total time for the round trip. then if t is the total time round trip and d is the distance between A and B, then it would satisfy

2d = 63t

with any other speed on the flats, i do not see how he could calculate d given the information he has.

Originally posted by davegage
I think Peakite is right and the answer is 63...
...
but we can say this much: if he drives 63 miles per hour on the flat, then he can very simply calculate the distance between A and B with the given information. In fact, i think he w ...[text shortened]... the distance between A and B, then it would satisfy

2d = 63t

That is correct, davegage!

He can work out the distance from A to B if he takes the same amount of time to go x miles flat & back as he does to go x miles uphill and x miles downhill.

To put it another way,
if
the downhill speed is d
and the uphill speed is u
the flat speed must be 2du/(d+u)

That is, d, f, u, must be in harmonic progression.

Originally posted by THUDandBLUNDER
That is correct, davegage!

He can work out the distance from A to B if he takes the same amount of time to go x miles flat & back as he does to go x miles uphill and x miles downhill.

To put it another way,
if
the downhill speed is d
and the uphill speed is u
the flat speed must be 2du/(d+u)

That is, d, f, u, must be in harmonic progression.

Good enough for the puzzle, but not very natural. In real life, one spends less time going back and forth on a flat road than on a road with hills. Which would be obtained more likely with with the average of the two speeds.