I don't get this question could someone help please

A vacuum cleaner has a power rating of 600W

For how many hours was the vacuum cleaner used if the cost of operating the vacuum cleaner was $6.36?

The cost of electricity is $0.2650 per kilowatt-hour.

A part of the trouble is that I don't understand the term kilowatt-hour.

Guest Aug 12, 2015

#3**+10 **

**A vacuum cleaner has a power rating of 600W**

**For how many hours was the vacuum cleaner used if the cost of operating the vacuum cleaner was $6.36?**

**The cost of electricity is $0.2650 per kilowatt-hour.**

600 W = 0.6 kW

**$$\small{\text{$ \begin{array}{rcl} 0.6~ \mathrm{kW}\cdot t \cdot \left( \dfrac{\$0.2650}{\mathrm{kW\cdot h}} \right) &=& \$6.36 \\\\ 0.6\cdot t \cdot \left( \dfrac{0.2650}{\mathrm{h}} \right) &=& 6.36 \\\\ t &=& \dfrac{ 6.36 }{0.2650\cdot0.6}~ \mathrm{h} \\\\ \mathbf{t} & \mathbf{=} & \mathbf{40~\mathrm{h}} \\\\ \end{array} $}}$$**

**Check:**

**$$\small{\text{$ \begin{array}{rcl} 0.6~ \mathrm{kW}\cdot 40~ \mathrm{h} &=& 24 ~\mathrm{kW~ h}\\\\ 24 ~\mathrm{kW~ h} \cdot \dfrac { \$0.2650 } {\mathrm{kW~ h} } &=& \$6.36 \end{array} $}}$$**

heureka
Aug 12, 2015

#3**+10 **

Best Answer

**A vacuum cleaner has a power rating of 600W**

**For how many hours was the vacuum cleaner used if the cost of operating the vacuum cleaner was $6.36?**

**The cost of electricity is $0.2650 per kilowatt-hour.**

600 W = 0.6 kW

**$$\small{\text{$ \begin{array}{rcl} 0.6~ \mathrm{kW}\cdot t \cdot \left( \dfrac{\$0.2650}{\mathrm{kW\cdot h}} \right) &=& \$6.36 \\\\ 0.6\cdot t \cdot \left( \dfrac{0.2650}{\mathrm{h}} \right) &=& 6.36 \\\\ t &=& \dfrac{ 6.36 }{0.2650\cdot0.6}~ \mathrm{h} \\\\ \mathbf{t} & \mathbf{=} & \mathbf{40~\mathrm{h}} \\\\ \end{array} $}}$$**

**Check:**

**$$\small{\text{$ \begin{array}{rcl} 0.6~ \mathrm{kW}\cdot 40~ \mathrm{h} &=& 24 ~\mathrm{kW~ h}\\\\ 24 ~\mathrm{kW~ h} \cdot \dfrac { \$0.2650 } {\mathrm{kW~ h} } &=& \$6.36 \end{array} $}}$$**

heureka
Aug 12, 2015

#4**+5 **

Thanks Heureka

But I do not understand the term kilowatt hours either.

OR kilowatt for that matter.

What is a Watt? I mean I know it has something to do with power but I still don't get it. :(

Melody
Aug 12, 2015

#5**+5 **

In terms of electromagnetism, one watt is the rate at which work is done when one ampere (A) of current flows through an electrical potential difference of one volt (V).

And each rate of power is to multiply with the hour you use it.

heureka
Aug 12, 2015

#7**+5 **

The basic SI unit of Energy is the Joule (J).

One Joule per second is one Watt (W), a measure of power. W = J/s

One kilowatt (kW) is a thousand watts.

Power = Energy/time. Energy = Power*time.

A kilowatt-hour (kW-hr) is the energy expended by a power of one kilowatt for one hour.

1kW-hr = (1000J/s)*(3600s) = 3.6*10^{6} J.

You pay for energy used; in this case at a rate of 0.2650 dollars per kW-hr

.

Alan
Aug 12, 2015