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# If a machine consumes 5 kilowatts of power every t hours, how much pow

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If a machine consumes 5 kilowatts of power every t hours, how much pow  [#permalink]

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21 Feb 2018, 01:04
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If a machine consumes k/5 kilowatts of power every t hours, how much power in kilowatts, will three such machines consume in 10 hours?

A. 6t/k
B. t/k
C. 30kt
D. k/t
E. 6k/t

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Posts: 1090
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Re: If a machine consumes 5 kilowatts of power every t hours, how much pow  [#permalink]

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21 Feb 2018, 03:21
Bunuel wrote:
If a machine consumes k/5 kilowatts of power every t hours, how much power in kilowatts, will three such machines consume in 10 hours?

A. 6t/k
B. t/k
C. 30kt
D. k/t
E. 6k/t

k/5 in t hours

1 hour k/5t power consumed

10 hours 10k/5t = 2k/t

one machine consumes 2k/t in 10 hours .. 3 machines consume 6k/t

(E) imo
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If a machine consumes 5 kilowatts of power every t hours, how much pow  [#permalink]

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21 Feb 2018, 18:59
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Bunuel wrote:
If a machine consumes k/5 kilowatts of power every t hours, how much power in kilowatts, will three such machines consume in 10 hours?

A. 6t/k
B. t/k
C. 30kt
D. k/t
E. 6k/t

Rate and algebra
The fractional number of kilowatts in the prompt might obscure the obvious: "___ kilowatts every ___ hours" is a rate.

What is the rate of consumption for one machine?
Number of kilowatts used: k/5
Per time unit: every t hours

Rate of consumption (no units after first term):
$$\frac{\frac{k}{5}kws}{t_{hours}}=(\frac{k}{5}*\frac{1}{t})=\frac{k}{5t}$$

At that rate, how much power will three such machines consume in 10 hours?

(Consumption rate) * (time spent consuming, 10 hrs) * (# of consumers, 3) = Total consumption
= Amount of power used

$$(\frac{k}{5t} * 10 * 3) = \frac{30k}{5t}=\frac{6k}{t}$$ kilowatts

Assign values
Assign values that result in integers.
Let k = 5
Let t = 1

Rate of power consumption
One machine consumes k/5 kilowatts of power every t hours

$$\frac{k}{5}kw=\frac{5}{5}kw = 1$$ kilowatt is consumed . . .
Every $$t = 1$$ hours
Consumption rate is $$\frac{1kw}{1hr}$$

How much power, in kilowatts, will three such machines consume in 10 hours?

(Consumption rate) * (# of machines) * (Time) = Total consumption

$$\frac{1kilowatt}{1hr} * 3 * 10hrs = 30$$ kilowatts

With k = 5, t = 1, find the answer choice that yields 30.

At a glance with mental math, eliminate B and D immediately (much too small), and C (huge). That leaves A and E

A. 6t/k: $$\frac{(6*1)}{5} = \frac{6}{5}$$. NO

E. 6k/t: $$\frac{(6*5)}{1} = \frac{30}{1} = 30$$. MATCH

*The eliminated options, which are indeed small or huge compared to 30:
B. t/k: $$\frac{1}{5}$$. NO

C. 30kt: $$(30)*(5)*(1) = 150$$. NO

D. k/t: $$\frac{5}{1} = 5$$. NO

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Re: If a machine consumes 5 kilowatts of power every t hours, how much pow  [#permalink]

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22 Feb 2018, 00:34
Bunuel wrote:
If a machine consumes k/5 kilowatts of power every t hours, how much power in kilowatts, will three such machines consume in 10 hours?

A. 6t/k
B. t/k
C. 30kt
D. k/t
E. 6k/t

i think answer is E if you assign value K as 10 and t as 1 then 1 machine will consume 2 kilowatts. So 3 machines will consume every hr 6 and for 10 hrs they will consume 60 total.
Only E will give us 60 as answer.
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Re: If a machine consumes 5 kilowatts of power every t hours, how much pow  [#permalink]

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22 Feb 2018, 01:25
Bunuel wrote:
If a machine consumes k/5 kilowatts of power every t hours, how much power in kilowatts, will three such machines consume in 10 hours?

A. 6t/k
B. t/k
C. 30kt
D. k/t
E. 6k/t

In t hours, power consumption of each machine = k/5
In 1 hr, power consumption of each machine = k/5t

In 10 hrs, power consumption of each machine = 10k/5t
In 10 hrs, power consumption of 3 machines = 30k/5t = 6k/t

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Re: If a machine consumes 5 kilowatts of power every t hours, how much pow  [#permalink]

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26 Feb 2018, 10:45
Bunuel wrote:
If a machine consumes k/5 kilowatts of power every t hours, how much power in kilowatts, will three such machines consume in 10 hours?

A. 6t/k
B. t/k
C. 30kt
D. k/t
E. 6k/t

The rate of 3 machines is 3 x (k/5)/t = 3k/5t

Thus, in 10 hours the amount of power consumed will be 3k/5t x 10 = 30k/5t = 6k/t.

Alternate Solution:

If one machine consumes k/5 kilowatts every t hours, then three machines will consume 3k/5 kilowatts every t hours.

We can set up a proportion and solve for x:

(3k/5)/t = x/10

30k/5 = xt

6k = xt

x = 6k/t

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Re: If a machine consumes 5 kilowatts of power every t hours, how much pow  [#permalink]

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11 Mar 2019, 08:16
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Re: If a machine consumes 5 kilowatts of power every t hours, how much pow   [#permalink] 11 Mar 2019, 08:16
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