[ebaines]

OK - another fun little math problem for you to think about. This is one of my favorite math riddles because it sounds complicated but is really quite simple.

A man is in the habit of taking the train from work to his home town every day. The train always gets to his home town station precisely at 6:00 PM (hey, it's a math problem, so everything always works perfectly). Now this guy is rather rich, and he has a chauffeur who meets him at the train station every day at 6:00 to take him home. Every day the chauffer drives from the man's home to the station to meet his boss, and he has the timing down so well that he arrives at the station at the same time as the man gets off the train, so there's no idle time for either the chauffeur or the man. Every day after the man gets picked up they drive directly home, and they always arrive at home at exactly the same time every day.

Well one day the man decides to alter his routine, and he takes a train that gets in an hour early. But he forgets to call ahead to tell the chauffer to meet him early. When he gets off the train there is of course no car waiting, so the man decides to start walking home. After a while the chauffeur comes driving along, sees the man walking along the road, stops to pick him up, and the two drive on home.

When they get home the man walks in the door and his wife says, "Honey, what a nice surprise! You're home 20 minutes early!"

Question - how long was the man walking along the road before the chauffeur stopped to pick him up?

Hint - if you find yourself trying to solve this using simultaneous equations in multiple unknowns you aren't thinking about it right - there's a simpler way.

[J_9]

Oh, jeez math!!

40 minutes?

[Capuchin]

Hmmm... 50 minutes?. Yes I think that's right..

[J_9]

Well if the train gets in an hour early, that is 60 minutes, and he is home 20 minutes early, wouldn't that mean he was walking for 40 minutes?

[ebaines]

Cap is right on!

[J_9]

Okay, I have to know how that works!!

He leaves 60 minutes early, gets home 20 minutes early

Okay, I am lost

[Capuchin]

His chauffeur saves 20 minutes... 10 minutes in each direction, so the guy must have been walking until 5:50

[eeseely]

I would suggest that this problem has no answer.

Here's my approach:

GIVEN:

Tc = Driving time (Station to Home) (hours

Normal arrival time = Tn = Tc + 6 (hours)

Today's Arrival time = T = Tn – 1/3 (hours)

T = 5 + k*Tc + Walk Time (hours)

5 + k*Tc + Walk Time = Tn – 1/3 (hours)

5 + k*Tc + Walk Time = Tc + 6 - 1/3 (hours)

WT = Tc*(1-k) + 6 – 5 -1/3 (hours)

WT = Tc*(1-k) +2/3 (hours)

Substitute for Tc:

Wt = (Tn – 6) (1-k) + 1 (hours)

WT = Tn –6 +6k –k*Tn + 1 (hours)

We don't know what time he normally gets home

[Capuchin]

Do you not agree that my answer is logical?

He gets home 20 minutes early, so his chauffer must pick him up 20/2 minutes earlier than normal.

[ebaines]

eeseely:

You are correct that we don't know what time he normally gets home, and neither do you know your factor "k", but these are not needed to solve the riddle. Looks to me like for your approach to work you need to know both pieces of data. Since we don't know either of these, you need tro try a different approach!

[eeseely]

When I have time, I'll take another look at your riddle.

[H_Thomas]

OK - another fun little math problem for you to think about. This is one of my favorite math riddles because it sounds complicated but is really quite simple.

A man is in the habit of taking the train from work to his home town every day. The train always gets to his home town station precisely at 6:00 PM (hey, it's a math problem, so everything always works perfectly). Now this guy is rather rich, and he has a chauffeur who meets him at the train station every day at 6:00 to take him home. Every day the chauffer drives from the man's home to the station to meet his boss, and he has the timing down so well that he arrives at the station at the same time as the man gets off the train, so there's no idle time for either the chauffeur or the man. Every day after the man gets picked up they drive directly home, and they always arrive at home at exactly the same time every day.

Well one day the man decides to alter his routine, and he takes a train that gets in an hour early. But he forgets to call ahead to tell the chauffer to meet him early. When he gets off the train there is of course no car waiting, so the man decides to start walking home. After a while the chauffeur comes driving along, sees the man walking along the road, stops to pick him up, and and the two drive on home.

When they get home the man walks in the door and his wife says, "Honey, what a nice surprise! You're home 20 minutes early!"

Question - how long was the man walking along the road before the chauffeur stopped to pick him up?

Hint - if you find yourself trying to solve this using simultaneous equations in multiple unknowns you aren't thinking about it right - there's a simpler way.

40 minutes. I want to know

[Skell]

Cap is right. Sorry Cap, had to spread the love.

Why are you guys trying to solve it? The answer is already here in the thread.