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A motor draws
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09 Apr 2021, 05:09
09 Apr 2021, 05:09
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50% (04:17) correct
50% (03:03) wrong based on 4 sessions
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A moto draws 15 kw (kilowatts) of power while it is running. During the 12-hour day shift, the motor kicks on four-time per hour and runs for 4 minutes every cycle. The motor runs at 85% efficiency (transmit 85% of the power into the equipment) during workday, with the remaining power being lost to heat and friction. During the 12-hour night shift, the motor switches to an operating scheme that runs 3 times per hour for 6 minutes every time. The night time efficiency is 74%. The power company rates are $0.14 per kw hours during the day and $0.11 per kw during the night. What is the total amount of money spent per day on wasted power (heat plus friction)?
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Show: :: OA
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Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: A motor draws
[#permalink]
09 Apr 2021, 08:42
09 Apr 2021, 08:42
2
During 12hr in daytime, the motor runs for 12 * 4 * 4 minutes, drawing 15 kW every hour.
So, power used during day \(= 15 * \frac{12 * 4 * 4 }{ 60} kW = 48 kW\)
But 100 - 85 = 15% of this power is wasted, since efficiency is 85%.
So, power wasted = 48 * 0.15 kW
Amount of money wasted @ 0.14$ = 48 * 0.15 * 0.14 = 1.008 (At this point, I have used calculator.)
Similarly, power used during night \(= 15 * \frac{12 * 3 * 6 }{ 60} kW = 54 kW\)
Power wasted = 100 - 74 = 26% of 54 kW = 0.26 * 54 kW
Amount of money wasted @ 0.11$ = 0.26 * 54 * 0.11 = 1.5444 (Here again, I have used calculator.)
Total amount of money wasted = 1.008 + 1.5444 = 2.5524
Hence, 2.55 is my answer.
So, power used during day \(= 15 * \frac{12 * 4 * 4 }{ 60} kW = 48 kW\)
But 100 - 85 = 15% of this power is wasted, since efficiency is 85%.
So, power wasted = 48 * 0.15 kW
Amount of money wasted @ 0.14$ = 48 * 0.15 * 0.14 = 1.008 (At this point, I have used calculator.)
Similarly, power used during night \(= 15 * \frac{12 * 3 * 6 }{ 60} kW = 54 kW\)
Power wasted = 100 - 74 = 26% of 54 kW = 0.26 * 54 kW
Amount of money wasted @ 0.11$ = 0.26 * 54 * 0.11 = 1.5444 (Here again, I have used calculator.)
Total amount of money wasted = 1.008 + 1.5444 = 2.5524
Hence, 2.55 is my answer.
gmatclubot
Re: A motor draws [#permalink]
09 Apr 2021, 08:42
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