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.

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:

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

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.    :(

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.

Thanks Heureka

I'm still confused but I probably always will be :/

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*10⁶ J.

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

.

Thanks Alan, I really like this answer.

I doubt that I have absorbed it but it is the only explanation of electricity that I have ever understood.  :))