There are 10^7 gallons of water in a lake. The owners of the lake want to remove the water at a rate of 10^3 gallons per hour.

Question

How many hours will it take to remove all the water?

Answer 1

Combine the terms, including dimensions, such that you are left with the desired dimension.

 

For example:  100 gallons X 25 gallons/minute = 2500 gallons² / minute  This obviously makes no sense.

 

to get a useful answer, we DIVIDE so that the unwanted units (dimensions) are cancelled:

    (100 gallons  ) / ( 25 gallons / minute ) = 4 minutes  (strike-thru shows the dimensions being cancelled)

 

 

Soooo:

10^7 gallons / (10^3 gallons / hour) = 10^4 hours

 

Remember:  when multiplying, add the exponents;  when dividing, subtract them

 

10^4 hours = 10,000 hours