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Company C has a machine that, working alone at its constant rate, proc
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23 May 2018, 07:33
23 May 2018, 07:33
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Company C has a machine that, working alone at its constant rate, processes 100 units of a certain product in 5 hours. If Company C plans to buy a new machine that will process this product at a constant rate and if the two machines, working together at their respective constant rates, are to process 100 units of this product in 2 hours, what should be the constant rate, in units per hour, of the new machine?
A. 50
B. 45
C. 30
D. 25
E. 20
A. 50
B. 45
C. 30
D. 25
E. 20
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Re: Company C has a machine that, working alone at its constant rate, proc
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23 May 2018, 07:45
23 May 2018, 07:45
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adkikani wrote:
Company C has a machine that, working alone at its constant rate, processes 100 units of a certain product in 5 hours. If Company C plans to buy a new machine that will process this product at a constant rate and if the two machines, working together at their respective constant rates, are to process 100 units of this product in 2 hours, what should be the constant rate, in units per hour, of the new machine?
A. 50
B. 45
C. 30
D. 25
E. 20
A. 50
B. 45
C. 30
D. 25
E. 20
Efficiency of Machine A = 20 units/hour
Efficiency of New Machine A = e units/hour
Now, we have \(( 20 + e )*2 = 100\)
So, \(20 + e = 50\)
Or, \(e = 30\), Answer must be (C)
Re: Company C has a machine that, working alone at its constant rate, proc
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26 May 2018, 20:09
26 May 2018, 20:09
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Expert Reply
adkikani wrote:
Company C has a machine that, working alone at its constant rate, processes 100 units of a certain product in 5 hours. If Company C plans to buy a new machine that will process this product at a constant rate and if the two machines, working together at their respective constant rates, are to process 100 units of this product in 2 hours, what should be the constant rate, in units per hour, of the new machine?
A. 50
B. 45
C. 30
D. 25
E. 20
A. 50
B. 45
C. 30
D. 25
E. 20
The rate of the current machine, \(M_1\),
plus the rate of the new machine, M\(_2\),
must = \(\frac{100u}{2hrs}\).
Hence express M\(_1\)'s rate in "per 2 hours"
Work rate of M\(_1\)?
\(\frac{100}{5hrs}=\frac{20}{1hr}=\frac{40}{2hrs}\)
\(M_1 + M_2 =\frac{100u}{2hrs}\)
\(\frac{40}{2} + M_2 = \frac{100}{2}\)
\(40 + 2*(M_2) = 100\)
\(2*(M_2) = 60\)
\(M_2 = 30\)
Answer C
Alternatively, two machines will produce
\(\frac{100u}{2hrs}=\frac{50u}{1hr}=50\) units per hour
Find M\(_1\)'s rate in units per 1 hour
\(M_1=\frac{100u}{5hrs}=\frac{20u}{1hr}=20\) per hour
Total Units needed per hour = 50
\(M_2\) must make up the difference
\(M_2\) must make (50 - 20) = 30 units per hour
Answer C
