## Who can help me with a tricky problem ?

Forum for the GRE subject test in mathematics.
greatgzz
Posts: 3
Joined: Sat Sep 22, 2012 5:06 am

### Who can help me with a tricky problem ?

A problem rather tricky...Please help me (not so much as GRE.but still college mathematics)

A turn-of -the-century bicycle has a front wheel with a diameter of 6 feet and a back wheel
with a diameter of 2 feet. When the bicycle rolls 600 PI feet in a straight line,
a. How far does a point on the tread of the back tire travel?
b. How far does a point on the tread of the front tire travel?
Justify your answers to (a) and (b).

vonLipwig
Posts: 51
Joined: Sat Mar 17, 2012 9:58 am

### Re: Who can help me with a tricky problem ?

This looks awfully like a question that you might have been assigned as homework, to me. Is it?

greatgzz
Posts: 3
Joined: Sat Sep 22, 2012 5:06 am

### Re: Who can help me with a tricky problem ?

vonLipwig wrote:This looks awfully like a question that you might have been assigned as homework, to me. Is it?

Sort of !!! it really drives me crazy...sigh...

Topoltergeist
Posts: 44
Joined: Tue Aug 09, 2011 6:18 pm

### Re: Who can help me with a tricky problem ?

I would experimentally verify my answer for this problem. I've always wanted to ride one of those crazy bikes ...

greatgzz
Posts: 3
Joined: Sat Sep 22, 2012 5:06 am

### Re: Who can help me with a tricky problem ?

Topoltergeist wrote:I would experimentally verify my answer for this problem. I've always wanted to ride one of those crazy bikes ...

Wow...look forward to some insights about it
!!!

malaka
Posts: 7
Joined: Tue Sep 04, 2012 3:45 am

### Re: Who can help me with a tricky problem ?

Topoltergeist wrote:I would experimentally verify my answer for this problem. I've always wanted to ride one of those crazy bikes ...

Really i am also crazy for rideing.

tarheel
Posts: 10
Joined: Wed Sep 26, 2012 4:37 pm

### Re: Who can help me with a tricky problem ?

greatgzz wrote:A problem rather tricky...Please help me (not so much as GRE.but still college mathematics)

A turn-of -the-century bicycle has a front wheel with a diameter of 6 feet and a back wheel
with a diameter of 2 feet. When the bicycle rolls 600 PI feet in a straight line,
a. How far does a point on the tread of the back tire travel?
b. How far does a point on the tread of the front tire travel?
Justify your answers to (a) and (b).

a. The back wheel rolls $600\pi /2\pi =300$ cycles. For each cycle, the distance that the point moves equals to the length of the cycloid, which equals 4*diameter=8 feet. Totally, it travels 8*300=2400 feet.

b. Using the same method as a). The answer is the same.

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