wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> easy >> Buses
        
(Message started by: Nootch on Sep 8^th, 2004, 11:53am)

Title: Buses
Post by Nootch on Sep 8^th, 2004, 11:53am

On route 71X buses start from the Green Man at Ilworth and ply backwards and forwards between hostlry and the Shabby Tiger at Plugstead. There are 11 buses on this route; each, on arriving at either terminus, waits for one minute and then begins the return journey.

Mr. Brightly, a bus driver from the provinces, boarded a bus at Green Man that other day and road all the way to Shabby Tiger, making a note every time he passed a 71X bus. He passed on (so he calculated) every 1,320 yards, and estimated their average speed at 15 m.p.h

How many buses did he pass en route?
;D

Title: Re: Buses
Post by Grimbal on Sep 8^th, 2004, 4:08pm

Ouch! Can you convert that into metric? Kilometers and kilometers per hour?

Would make life easier for us Europeans. ;D ;D

Title: Re: Buses
Post by asterix on Sep 8^th, 2004, 8:09pm

Not really. ;)

Title: Re: Buses
Post by THUDandBLUNDER on Sep 8^th, 2004, 11:59pm

on 09/08/04 at 16:08:07, Grimbal wrote:

Ouch! Can you convert that into metric? Kilometers and kilometers per hour?

Would make life easier for us Europeans. ;D ;D

...even for French-speaking Europeans who prefer Americanized spelling? ;)

Title: Re: Buses
Post by Patashu on Sep 9^th, 2004, 4:39am

Ow. Yards make my brain hurt. Owie.

How long is a yard anyway?

Title: Re: Buses
Post by John_Gaughan on Sep 9^th, 2004, 6:42am

He passed [hide]10[/hide] buses.

Title: Re: Buses
Post by THUDandBLUNDER on Sep 9^th, 2004, 7:55am

Quote:

...boarded a bus at Green Man that other day and road all the way to Shabby Tiger, making a note every time he passed a 71X bus.

on 09/09/04 at 06:42:16, John_Gaughan wrote:

He passed <hidden> buses.

But he travelled only half the route. Were all 10 coming the other way?

Title: Re: Buses
Post by John_Gaughan on Sep 9^th, 2004, 8:50am

No, but that is irrelevant. Start at the beginning. As he leaves, the bus directly behind him arrives next. They pass just a few minutes into the journey. A few minutes later he passes the bus two behind him, and so on. The last bus he passes right before pulling into the destination is the one in front of him, which departs right before he arrives.

Imagine a rubber band stretched between two small pulleys. There are eleven tick marks evenly spaced along the rubber band. As the pulleys turn, moving the band, each tick mark must pass each other mark once per half-revolution.

Title: Re: Buses
Post by John_Gaughan on Sep 9^th, 2004, 8:55am

on 09/09/04 at 07:55:05, THUDandBLUNDER wrote:

But he travelled only half the route. Were all 10 coming the other way?

Sorry, I did not quite address your question. Yes, all ten were coming the other way, at some point during his journey, but not necessarily the entire time. It only takes a second or two to pass, remember.

Think of a unit circle. Pick eleven unique half-circles. Assume one, our bus driver, is on the half-circle that starts at -1 and goes up to 1. Every other half-circle must have a portion that is decreasing. They cannot be strictly non-decreasing. So at some point on the arc, they are "coming the other way."

Title: Re: Buses
Post by THUDandBLUNDER on Sep 9^th, 2004, 9:37am

Yes, John, you are right.

Title: Re: Buses
Post by Grimbal on Sep 9^th, 2004, 11:21am

on 09/08/04 at 20:09:38, asterix wrote:

Not really. ;)

That's why I put the 2 smileys...