Math Is Fun Forum

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

olympiad problems

1. A train travelling 30mph reaches a tunnel which is 9 times as long as the train. If the train takes 2 minutes to clear the tunnel, how long is the train in feet?
first 2/60 = 1/30 of an hour, thus the train travels 1 mile. Thus the tunnel is 1 mile. 5280 miles divided by 9 = 586.6666 reperating, so the train is 586.6 feet.
2. If x - y + 2z, and x+z = y + t, and y + t+z, how many z's = x?
3. a athelete running 100 meters or 200 meters does not reach top speed until 40 miles. In a 200 meter race a certain runner's time is 5.4 secs and his time for 100 meter s is 10 secs.Assuming he maintains full speed from 40 meters to the end of the reae, what would be his time for 200 meters?

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Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Re: olympiad problems

I need serious help on number 3

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The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: olympiad problems

40 miles.

40 meters instead maybe?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: olympiad problems

In a 200 meter race a certain runner's time is 5.4 secs and his time for 100 meter s is 10 secs.

Defies logic.

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,641

Re: olympiad problems

hi Mathegocart

Q1 ?  The key words here are 'reaches' and then 'clears'.  The front end reaches but the rear end clears.  If the train is 'd' long and the tunnel is 9d long then the rear end of the train has travelled d + 9d when it clears the tunnel. So divide by 10 not 9.

Q2. ?

If x - y + 2z, and x+z = y + t, and y + t+z, how many z's = x?

Do you mean

x-y+2z = x + z = y + t = y + t + z

No.  That's silly.  I think the EQUALS and AND signs are misplaced here.

Q3.

a athelete running 100 meters or 200 meters does not reach top speed until 40 miles

Do you mean "An athlete running either 100 metres or 200 metres reaches a top speed after he has run 40 metres."  In which case are we to assume that he accelerates at a constant rate until this moment?  Alternatively, it would be possible (but it's a tougher calculation) to have a steadily dropping rate of acceleration until it is zero after 40 metres. 

Then

In a 200 meter race a certain runner's time is 5.4 secs and his time for 100 meter s is 10 secs.

  That's clever   I'm hoping this has a typo because it's a strange running model otherwise, and a new Olympic record!

And finally

what would be his time for 200 meters?

Eh!  Isn't it 5.4 secs ?  You seem to have a serious gremlin infestation in this question. 

Bob

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Sometimes I deliberately make mistakes, just to test you!  …………….Bob