Conveyor Belt Problem

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preludelong: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sun May 17, 2009 9:03 pm; Thanked: 1 times

Conveyor Belt Problem

by preludelong » Thu Jun 04, 2009 8:41 pm

Hello

I am having trouble with this problem. Could someone be kind enough to help me solve the problem?

As shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around two circular wheels each 1 foot in diameter. What is the distance, in feet, between the centers of the two wheels?

a) (15- π)/2

b) 5π/4

c) 15- 2π

d) 15 - π

e) 2π

the answer is A

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Source: Beat The GMAT — Problem Solving | Thu Jun 04, 2009 8:41 pm

rah_pandey: Master | Next Rank: 500 Posts; Posts: 122; Joined: Fri May 22, 2009 10:38 pm; Thanked: 8 times; GMAT Score:700

by rah_pandey » Thu Jun 04, 2009 11:18 pm

Length of belt=15 foot given

length covering circular part(one cylinder)= half of circumfrence
2*pi*r/2(since half circle)
=pi*r
r=1/2

total length of belt on circular part is 2*pi*r=pi (since r=1/2)

now remaining length=15-pi

distance between centers= (15-pi)/2

remember since both circles have same radius therefore the belt leaves the circle after half circle. If cylinders of diff radii would have been used than we could not have taken point of belt leaving the circle at half circle.

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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

Re: Conveyor Belt Problem

by dtweah » Fri Jun 05, 2009 9:15 am

preludelong wrote:Hello

I am having trouble with this problem. Could someone be kind enough to help me solve the problem?

As shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around two circular wheels each 1 foot in diameter. What is the distance, in feet, between the centers of the two wheels?

a) (15- π)/2

b) 5π/4

c) 15- 2π

d) 15 - π

e) 2π

the answer is A

Combine the 2 semicircles where the belt curves into one circle and find the circumference.

C=2pi r= 2 pi x 1/2=Pi
Take pi from 15 and get 15-pi. You are left with the upper belt and lower belt of the same lenght summing to 15-pi. But you only want one one of them which gives the distance you are looking for. So you have to divide by 2, hence the answer.