Lara employed a residential cleaning service to tidy up her home. They charged her $150 for 3 hours of work. Her neighbor, Roy hired the same agency and paid them $225 for their services.
How many hours did they take to complete the job at Roy's home?

Step-by-step explanation:

Find the rate that was charged for Lara's time

       rate = dollars / hour

The use this rate to calculate how many hours it took to clean Roy's house, since the rates are the same.  Solve for hours

      rate for Lara = dollars / hour        =  $150 / 3 hour   =     $50 / hour

     rate for Roy = dollars / hour         Solve for hours

                                                            multiply both sides by hours

     (rate for Roy) (hour) = (dollars / hour) (hour)

     (rate for Roy) (hour) = (hour) (dollars / hour)       right side hours cancel

     (rate for Roy) (hour) = (dollars)     divide both sides by (rate for Roy)

     (rate for Roy) (hour) / (rate for Roy) = (dollars) / (rate for Roy)

                       now the rate for Roy on the leftside cancel

     (rate for Roy) (hour) / (rate for Roy) = (dollars) / (rate for Roy)

     (hour) = (dollars) / (rate for Roy)           Plug in $225 charged to Roy

                                                                     and the $50 / hour rate

       hour = $225 / ($50/hour)             ( 1 over 1 / hour )  = hour  

                = $(225/50) hour            think about  1 / (1/2)  = 2  the same with units

      hour =  4.5 hours

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