Simple Unit Analysis for Generator Revenue Calculation

[ainster31]

Homework Statement

$$Let\quad n\quad =\quad the\quad number\quad of\quad hours\quad I\quad run\quad a\quad 40\quad kilowatt\quad generator.\\ Assume\quad that\quad it\quad costs\quad $0.08\quad for\quad 1\quad kWh.\\ Revenue\quad from\quad generator=\frac { $0.08 }{ kW\cdot hours } \quad (40\quad kW)\quad (n\quad hours)\\ =$3.2n\\ \\ Suppose\quad I\quad want\quad to\quad make\quad $6.40\quad from\quad the\quad generator.\\ $6.4=$3.2n\\ n=2$$

Homework Equations

The Attempt at a Solution

What am I doing wrong? Why isn't n in hours?

 

[Dick]

Homework Statement

$$Let\quad n\quad =\quad the\quad number\quad of\quad hours\quad I\quad run\quad a\quad 40\quad kilowatt\quad generator.\\ Assume\quad that\quad it\quad costs\quad $0.08\quad for\quad 1\quad kWh.\\ Revenue\quad from\quad generator=\frac { $0.08 }{ kW\cdot hours } \quad (40\quad kW)\quad (n\quad hours)\\ =$3.2n\\ \\ Suppose\quad I\quad want\quad to\quad make\quad $6.40\quad from\quad the\quad generator.\\ $6.4=$3.2n\\ n=2$$

Homework Equations

The Attempt at a Solution

What am I doing wrong? Why isn't n in hours?

Because when you write time=n*hours, the units are in the "hours" part and n itself is dimensionless. If you the units to be included in 'n' just write time=n.

 

[ainster31]

Because when you write time=n*hours, the units are in the "hours" part and n itself is dimensionless. If you the units to be included in 'n' just write time=n.

Ah, got it. Thanks.