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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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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

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

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23 May 2018, 07:45
1
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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26 May 2018, 20:09
1
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$$_1$$?
$$\frac{100}{5hrs}=\frac{20}{1hr}=\frac{40}{2hrs}$$

$$M_1 + M_2 =\frac{100u}{2hrs}$$

$$\frac{40}{2} + M_2 = \frac{100}{2}$$

$$40 + 2*(M_2) = 100$$
$$2*(M_2) = 60$$
$$M_2 = 30$$

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

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

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10 Aug 2018, 05:56
1
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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10 Aug 2018, 07:28
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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05 Sep 2018, 21:43
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)
Re: Company C has a machine that, working alone at its constant rate &nbs [#permalink] 05 Sep 2018, 21:43
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