Brain Teaser - Charlie Leaves School Early

[JVY]

A little puzzle that I spotted somewhere recently and thought it might be fun to post on here:

Charlie finishes school each day at 3.30pm. Each day, his mum drives the same route to school to pick him up at 3.30pm. One day, school finishes early at 3.00pm. Charlie’s mum has forgotten about this and when he leaves the school and sees his mum isn’t there, he decides to walk home along the same route his mum always drives. Luckily, on the way to school, his mum sees Charlie, picks him up and drives him home. They arrive home 10 minutes earlier than usual.

For how many minutes was Charlie walking before he got picked up by his mum :?:

 

[rockdemon]

typo there? Leaves early at 3.30?

 

[JVY]

Thanks Rich - have sorted the typo.

 

[Pilkie]

Mum may have a 30 min or 1 hr drive to pick him up!!
Will be interesting to see the math solution?
But I reckon its about 10 minutes! :?

 

[Geordie Jim]

His mum saved ten minutes on her round trip, so one way 5 min. She met him at 25 past so he was walking for 25 minutes??

 

[John]

I don't think he walked far, but when mum found him all the other mums had gone, so she wasn't rabbitting on for 20 mins before she left the school and cleared the obstruction caused by her Discovery double parked on the yellow zig zags. 3 mins max, as he will only live 6 mins from school but his mother's such a lazy mare she wont walk it.


John.

 

[quattro]

I am going to have to agree with Jim, 25 minutes.

Richard

 

[rockdemon]

i make it 20 minutes....

Charlie walks the same as 10 minutes by car before being picked up. That means that the car would take 10 minutes more to get to school to get there for 3.30?

Rich

 

[Whitewash]

But we are all missing the big issue here!!!!!!!

Charlie could have been kidnapped,we all know its unsafe for kids to be walking the street, their cotton wool might fall off! kids will almost certaining get round eyes from not staring at a computer screen for the time it takes to walk home!

 

[Pilkie]

Blatant parental neglect!!
Anyway how do we know she drove from home to pick him up?
Could of been on the way home from work! :wink:

And I cant find it on the teaserintnet either!!

 

[JVY]

I reckon Geordie Jim & Richard quattro are right. Quite like the other answers though which seem to be equally valid . When I went to school, pretty much only a few teachers' cars were parked outside the school in the morning and virtually every kid walked. Oh how times have changed. I'm ashamed to say that my missus drives the little ones to school even though you can see the school from our house :roll: . If I'm off work and take them to school I insist on walking - boy do they complain :!: .

 

[darth sidious]

i make it 20 minutes....

Charlie walks the same as 10 minutes by car before being picked up. That means that the car would take 10 minutes more to get to school to get there for 3.30?

Rich

I'm tending to 20 minutes too, but not totally convinced that my reasoning is correct!

 

[darth sidious]

I reckon Geordie Jim & Richard quattro are right. Quite like the other answers though which seem to be equally valid . When I went to school, pretty much only a few teachers' cars were parked outside the school in the morning and virtually every kid walked. Oh how times have changed. I'm ashamed to say that my missus drives the little ones to school even though you can see the school from our house :roll: . If I'm off work and take them to school I insist on walking - boy do they complain :!: .

Do you have the right answer?

 

[rockdemon]

His mum saved ten minutes on her round trip

Think this is a question of interpretation... to me it's not the round trip it means, it means 10 minutes earlier than if they'd left the school gate at 3.30...

Rich

 

[JVY]

My thinking was the same as Geordie Jim's - that if they got home ten minutes earlier than usual, 5 minutes were saved on the way to school and 5 minutes were saved on the way home. This means that Charlie's mum must have found him 5 minutes before she would normally arrive at the school. She normally arrives at school at 3.30pm, so she must have found him at 3.25pm. So, if Charlie left at 3.00pm, he must have been walking for 25 minutes.

 

[vin-kohler]

His mum saved ten minutes on her round trip, so one way 5 min. She met him at 25 past so he was walking for 25 minutes??

Definitely the correct answer. And I love Geordie Jim's concise wording. But drop the doble questionmark please!
Vin Kohler

 

[darth sidious]

His mum saved ten minutes on her round trip, so one way 5 min. She met him at 25 past so he was walking for 25 minutes??

Definitely the correct answer. And I love Geordie Jim's concise wording. But drop the doble questionmark please!
Vin Kohler

Please elaborate on how YOU think it's the correct answer.

i.e. PROVE IT!

I'm not quite convinced that round-trip is the right way of thinking. It doesn't specifically state that she makes a start from the home, or that she makes a "loop" i.e. round-trip

 

[v8guy]

My view on this is that you can only come to a difinative answer in a perfect world when nothing changes day to day. As many of us make the same trips on daily basis and I bet no trip is identical in time. There are to many factors involved, weather, traffic, accidents etc etc.
Sorry for going all serious

 

[darth sidious]

My view on this is that you can only come to a difinative answer in a perfect world when nothing changes day to day. As many of us make the same trips on daily basis and I bet no trip is identical in time. There are to many factors involved, weather, traffic, accidents etc etc.
Sorry for going all serious

Yes, a very true and valid point! We assume a perfect world in these problems.

What I'm asking for is an explanation as to why 25 minutes is the correct answer, as opposed to just "yes, 25 minutes is right"

 

[vin-kohler]

The implicit assumtion is "a perfect world", i.e. constant speed and no time lost at the reversal point.

Coming to the proof: A convenient way to visualize this kind of problems is to draw a graph with time on the horizontal and distance on the vertical axis. The slope of a line will then be the speed. Positive slope -> one direction, negative slope -> opposite direction. Steep slope -> fast movement (much distance covered in little time).

Looking at my graph: Normally mother drives from home to point P, thence with the same speed but negative slope back home. Today she turns back at point Q. If you now watch the little triangle at the top of the drawing you can see that (because of the symmetry) Q is just half of ten minutes earlier than P. That is the pickup time is 3:25.

You may now even draw a line from where the boy leaves school at 3:00 to point Q, to infer that his walking speed is 1/5 of mother's driving speed.

Happy now? Or do wish to have all that in a more formular/abstract representation?

Now I only hope that I manage to add my graph attachment.

Greetings
Vin Kohler