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#920854 - 10/27/13 11:40 AM Travelling...
CanukDenis Offline
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Registered: 11/26/00
Posts: 14910
Loc: Ottawa Ontario Canada
Art, Ben and Cam travel a 10 mile straight path.

They have a bike and a skateboard.

All 3 walk at 5 mph.

Anyone on bike goes 15 mph, on skateboard goes 6 mph.

They leave at same time, and arrive at end of path at same time.

What is shortest possible time?

NO TRICKS like double riding, carrying skateboard while biking...
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#920894 - 10/27/13 03:53 PM Re: Travelling... [Re: CanukDenis]
BobH Offline
Addicted Boomer

Registered: 10/14/11
Posts: 1371
Loc: 47.79N, 122.24W
Here's my answer. I hid it in case it is right and someone else wants to solve as well.
Click to reveal..

I'm going to say 2 hours. One has to be walking at all times and anyone that will hand off the skateboard or bicycle has to be back alongside the walker to do it. So the last person can never be faster than as if he walked the whole way. As they all arrive together it must be at the walking pace, therefore 2 hours.
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#920905 - 10/27/13 05:27 PM Re: Travelling... [Re: CanukDenis]
CanukDenis Offline
Adept Boomer

Registered: 11/26/00
Posts: 14910
Loc: Ottawa Ontario Canada
Good try Bob; can be done much faster...
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#920927 - 10/27/13 07:41 PM Re: Travelling... [Re: CanukDenis]
Urban Worrier Offline

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Registered: 11/16/04
Posts: 13859
Loc: Bucks, England
I can do it in 100 minutes, but only if Art is allowed a comfort break when he changes mode of transport. Guess that counts as TRICKS huh? hardwall
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#920935 - 10/27/13 08:52 PM Re: Travelling... [Re: CanukDenis]
CanukDenis Offline
Adept Boomer

Registered: 11/26/00
Posts: 14910
Loc: Ottawa Ontario Canada
No, that wouldn't be a trick, since there is
nothing in the wording that prevents a "rest".

However, can be done in less than 100 minutes,
plus (in my solution) no one takes a rest.
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#920945 - 10/27/13 10:10 PM Re: Travelling... [Re: CanukDenis]
manxman Offline
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Registered: 07/23/02
Posts: 13904
Loc: Unionville
13/9 hours think
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#920948 - 10/27/13 10:41 PM Re: Travelling... [Re: CanukDenis]
CanukDenis Offline
Adept Boomer

Registered: 11/26/00
Posts: 14910
Loc: Ottawa Ontario Canada
13/9 * 60 = 86 2/3 minutes: beats my solution slightly....

How did you get that?
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#920984 - 10/28/13 08:10 AM Re: Travelling... [Re: CanukDenis]
manxman Offline
Adept Boomer

Registered: 07/23/02
Posts: 13904
Loc: Unionville
Not sure if it is solid reasoning but.....
1. walking the 10 miles takes 2 hours
2. biking the 10 miles takes 2/3 hours
3. skateboarding the 10 miles takes 5/3 hours
Since all three people must be doing one of the three at all times then the total times divided by 3 should be how long it takes for everything to get there.
2+2/3 + 5/3 = 13/3
13/3 /3 =13/9
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#920990 - 10/28/13 08:28 AM Re: Travelling... [Re: CanukDenis]
CanukDenis Offline
Adept Boomer

Registered: 11/26/00
Posts: 14910
Loc: Ottawa Ontario Canada
Good thinking, but will not work in practice.

Say Art starts off with bike: he is always ahead of
Ben and Cam while on the bike; so when he gets off,
he must leave the bike and start walking.

So the bike will not be used for a while, until
Ben or Cam get to it...

Ok?
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#921002 - 10/28/13 10:35 AM Re: Travelling... [Re: CanukDenis]
manxman Offline
Adept Boomer

Registered: 07/23/02
Posts: 13904
Loc: Unionville
Ok. I thought there was a flaw. Thanks smile
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#921021 - 10/28/13 12:58 PM Re: Travelling... [Re: CanukDenis]
CanukDenis Offline
Adept Boomer

Registered: 11/26/00
Posts: 14910
Loc: Ottawa Ontario Canada
HINT:
2 of the guys arrive at the 10mile point walking,
while the other arrives on the bike.
So the skateboard is not used all the way.
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#921193 - 10/29/13 02:16 PM Re: Travelling... [Re: CanukDenis]
CanukDenis Offline
Adept Boomer

Registered: 11/26/00
Posts: 14910
Loc: Ottawa Ontario Canada
Hint#2:
After the bike is left by whoever uses it first, it
remains unused for 32 minutes before being used again.
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I'm a man of few words...but I use them often

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#921354 - 10/30/13 01:22 PM Re: Travelling... [Re: CanukDenis]
CanukDenis Offline
Adept Boomer

Registered: 11/26/00
Posts: 14910
Loc: Ottawa Ontario Canada
Hint#3:
the guy who starts off using the skateboard
leaves it after a few miles; not used after.
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#921799 - 10/31/13 10:52 PM Re: Travelling... [Re: CanukDenis]
CanukDenis Offline
Adept Boomer

Registered: 11/26/00
Posts: 14910
Loc: Ottawa Ontario Canada
OK; 88 minutes is the time.

HOW? happydance
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#922019 - 11/02/13 11:11 AM Re: Travelling... [Re: CanukDenis]
CanukDenis Offline
Adept Boomer

Registered: 11/26/00
Posts: 14910
Loc: Ottawa Ontario Canada
In case I forget...
Click to reveal..

Assume Art starts on bike, Ben by walking, Cam on skate board

Art: 4 miles on bike[1], 6 miles walking
Ben: 4 miles walking, 4 miles on bike[2], 2 miles walking
Cam: 8 miles on skateboard[3], 2 miles on bike

[1]: bike left for 32 minutes
[2]: bike left for 16 minutes
[3]: skateboard remains behind

Art: 16 + 72 = 88
Ben: 48 + 16 + 24 = 88
Cam: 80 + 8 = 88
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