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Company C has a machine that, working alone at its constant rate

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Company C has a machine that, working alone at its constant rate  [#permalink]

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New post 23 May 2018, 06:33
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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

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Re: Company C has a machine that, working alone at its constant rate  [#permalink]

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New post 23 May 2018, 06:45
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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


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)
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Company C has a machine that, working alone at its constant rate  [#permalink]

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New post 26 May 2018, 19:09
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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

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
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Re: Company C has a machine that, working alone at its constant rate  [#permalink]

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New post 10 Aug 2018, 04:56
1
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


Company C has a machine that, working alone at its constant rate, processes 100 units of a certain product in 5 hours.

Rate = 1/5

Another machine = 1/x

Togather 1/5+1/x=1/2

x=3.333

constant rate, in units per hour, of the new machine = 100/3.33 = 30

Hence C

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Re: Company C has a machine that, working alone at its constant rate  [#permalink]

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New post 10 Aug 2018, 06:28
Yes NandishSS - you are absolutely right!

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Re: Company C has a machine that, working alone at its constant rate  [#permalink]

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New post 05 Sep 2018, 20:43
Machine A(old machine) can produce 100 units in 5 hour so in 1hour it can produce is 20 units.
Total requirement is of 100 units in 2 hours.. So 100- Out put of Machine A in 2 hrs=60 units.
To manufacture 60 units in 2 hrs new machine should produce 30 units ...
Ans:C 30units (new machine output/hr)
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Re: Company C has a machine that, working alone at its constant rate &nbs [#permalink] 05 Sep 2018, 20:43
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Company C has a machine that, working alone at its constant rate

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