Quiz: Johnny come early. Contributed by Marcelo Branco

[drsarao]

Hi All,
The Quiz below was PMed to me for proof reading and subsequent posting (Marc is vacationing). It is pasted more or less as posted to me.
(I do NOT know the answer!) (Marc will be back AFTER 2 weeks)
All are however, encouraged to take part.

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John is a methodical guy.

Every day, returning home, he takes the same train.
At the exact moment that the train reaches the station, his driver also comes with the car. He then gets into the car and goes home.

One day he leaves work an hour early, and therefore arrives at the station an hour earlier than usual.
To save time, begins to walk by the same path used by his driver.

Finds his car at some point on the way. The car makes a U-turn and takes him home.

Upon arriving home, he notes that he arrived 20 minutes earlier than usual.

Assuming no loss of time in the U-turn, for how long did John walk to find his car?
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(I do NOT know the answer!) (Marc will be back AFTER 2 weeks)
All are however, encouraged to take part.

Previous Quiz: The-age-of-three-daughters

 

[Kyle123]

I reckon 10 minutes

 

[Eric Golf]

I think he walked for 50 minutes

Eric.

 

[Domski]

How did you proof read it without knowing the answer Dom

 

[JamesW]

40 minutes.







**spoiler**


Say he arrives at 2PM on the early day. That would mean that on a normal day he arrives at 3PM. It must take him more than an hour to get home, otherwise on a normal day he would arrive home before, or as soon as, he gets to the station. So, lets say it takes him 90 minutes to get home on the early day and that would mean he gets home at 3:30PM, which we know is 20 minutes earlier than normal. This means he gets home at 3:50 on a normal day.

We now know that it took him 50 minutes to get home on a normal day, and 90 on the early day and 90-50 = 40.

You can use any number in place of the red number and still get the same result (assuming > 60).

What do I win?

 

[drsarao]

Dom,
Marc sent only the Quiz to proofread!

JamesW,
I followed pretty much similar logic using 60 and 120 minutes and arrived at 40 minutes.
No prizes as of now.
Another request goes out to Moderator(s)

I think the answer is right. Unless Marc throws in a 3rd dimension.

These kind of questions, we immediately jump to calculating the speed / distance / time etc.

 

[Eric Golf]

Since explanations are coming in I will give mine for still 50 mins.

Spoiler:


He gets back 20 mins early which means the cars round trip was 20 minutes shorter than normal i.e. it turned around 10 minutes short of the station.

He therefore met the car 10 minutes before it would have normally have picked him up, he arrived 1 hour early, so had walked for 50 minutes.

What do I win

 

[drsarao]

Eric,
Your explanation seems as convincing (more in fact).
As already stated, no prizes!
Waiting on Marc to deliver.

 

[Marcelo Branco]

Since explanations are coming in I will give mine for still 50 mins.

Spoiler:


He gets back 20 mins early which means the cars round trip was 20 minutes shorter than normal i.e. it turned around 10 minutes short of the station.

He therefore met the car 10 minutes before it would have normally have picked him up, he arrived 1 hour early, so had walked for 50 minutes.

What do I win

Eric,

Congratulations!!

M.

 

[Marcelo Branco]

Complete explanation

The answer is 50 minutes.

Let us reason together:
1. If John walked with the same speed as the car he would arrived one hour earlier.

2. As, in fact, he only arrived 20 minutes early, there was a delay (loss) of 40 minutes.

3. So we can conclude that the time John walked is 40 minutes longer than the car to do the same stretch.
John_Time = Car_time + 40

4. The car also arrived 20 minutes early. This is because the car did not travel, twice (round-trip) , the stretch that John walked.

5. So we can conclude that the car would take 20 minutes to make the round-about. And 10 minutes, half, to go through the stretch that John walked.
Important: assumes that the duration of travels of the car: from home to station and from station to home, are equal.

Final answer:
John_time = 10 + 40 = 50 minutes.

Is it clear?

M.