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Work Rate Problem

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by Abdulla » Thu Jun 18, 2009 3:16 pm
Machine A and machine B are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produce?

A) 6
B) 6.6
C) 60
D) 100
E) 110

OA is A
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by ssmiles08 » Thu Jun 18, 2009 4:13 pm
For Machine A, let r = rate, t = time.

r*t = 660

Machine B produces 10 hours less than A: t - 10
machine B's rate is 10% faster than A: 1.1r

(1.1r)(t - 10) = 660

set the equations equal to each other since they both equal 660

r*t = (1.1r)(t - 10)

rt = 1.1rt - 11r

1.1rt - rt - 11r = 0

.1t = 11

t = 110

r = 660/110 = 6

(A)
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by avanishjoshi » Thu Jun 18, 2009 11:01 pm
Let the capacity of machine A = A sprockets/hr
Let the capacity of machine B = B sprockets/hr
Let B work for X hours to produce 660 sprockets
Then A(X + 10) = B(X)

But B produces 10% more sprockets per hour than A .Therefore B = 1.1A.

A(X + 10) = 1.1A(X) = > X+10 = 1.1X = > X = 100.

[spoiler]A (100 + 10) = 660 => A = 6 which is the ANSWER[/spoiler]
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Re: Work Rate Problem

by dtweah » Fri Jun 19, 2009 2:59 pm
Abdulla wrote:Machine A and machine B are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produce?

A) 6
B) 6.6
C) 60
D) 100
E) 110

OA is A
660/ A -660/A+10= 10%(660/(A+10))
10(A+10) -10A =A
10A+100 -10A=A
A=100
660/110=6
Choose A.
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by Scott@TargetTestPrep » Tue Dec 12, 2017 6:37 am
Abdulla wrote:Machine A and machine B are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produce?

A) 6
B) 6.6
C) 60
D) 100
E) 110
We are given that machine A and machine B are each used to manufacture 660 sprockets; thus the work of each machine is 660. We also are given that it takes machine A 10 hours longer to produce 660 sprockets than it takes machine B, and that machine B produces 10% more sprockets per hour than machine A. If we let the rate of machine A = r, then the rate of machine B = 1.1r.

Since time = work/rate:

The time of machine A = 660/r and the time of machine B = 660/(1.1r) = 600/r

Since machine A takes 10 hours longer to produce 660 sprockets than does machine B, we can create the following equation and determine r:

660/r = 600/r + 10

60/r = 10

60 = 10r

6 = r

Thus, machine A produces 6 sprockets per hour.

Answer: A

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