BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Conveyor Belt Problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
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
Top
Source: — Problem Solving |
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.
Top
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.
Top
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Sun May 17, 2009 9:03 pm
Thanked: 1 times

by preludelong » Sun Jun 07, 2009 11:57 am
Thank you.
Top
Post new topic Post Reply
• Page 1 of 1