simple algebra word problem if it takes $5$ people $7$ hours to wash one building than how long does it take $4$? It takes $5$ window washers $7$ hours to wash one office building, how many hours would it take $4$ window washers to wash the building? 
This seems so simple, yet, when I work it out I get $5.6$ hours, which doesn't make sense, since you have less window washers it should take longer. 
If it takes $5$ window washers $7$ hours, than it takes $1$ window washer $1.4$ hours. 
 A: Hint:
One person would need $5\times7=35$ hours.
A: The error in your reasoning is found in your last sentence.  If it takes $5$ window washers $7$ hours to wash the windows in the building, then if each window washer works at the same rate, each window washer takes $7 \cdot 5 = 35$ hours to wash the windows when working alone since each window washer completes $1/5$ of the task and 
$$\frac{7~\text{h}}{\frac{1}{5}} = 7~\text{h} \cdot 5 = 35~\text{h}$$
Therefore, it a single window washer completes $1/35$ of the building in one hour.  
How much of the building will four window washers complete in one hour (assuming they each work at the same rate)?  Therefore, how many hours will it take four window washers to complete the entire building?
A: You could think about it like this:
$5$ people take $7$ hours to wash $1$ building
If you are dividing by $5$ you are dividing by the number of people
$1$ person takes $7$ hours to wash $1/5$ building
If you then divide by $7$ you are dividing by the number of hours
$1$ person takes $1$ hour to wash $1/35$ building
One person works at $1/35$ buildings per hour
If you divide the number of hours by the number of people you get something in the units $hp^{-1}$ - one fifth of a building takes $1.4$ hours per person for five people  - which is true, but not what you want to know.
A: So it takes $35$ man-hours to do the building.    
With $4$ men, the job will take $\dfrac {35}{4}$ hours.
