A student can read 1 page every 2 minutes. If every page has 80 words and the student reads for 3 hours, how many words will the student read

Question

A student can read 1 page every 2 minutes. If every page has 80 words and the student reads for 3 hours, how many words will the student read?

Answer 1

We may change the units without changing a value by using the Multiplicative Identity (that is, 1).  Any value multiplied by 1 remains the same.

 

This is called Dimensional Analysis,

 

For this problem, 

    1 = (1 page)/(2 minutes) = (2 minutes)/(1 page)                    [the reading rate]

    1 = (60 minutes)/(1 hour) = (1 hour)/(60 minutes)

    1 = (1 page)/(80 words) = (80 words)/(1 page)

 

  Note: You use the expressions that allow the units to cancel.

 

The student reads for 3 hours.

       3 hours

        (3 hours)*1                    [remains the same]

       (3 hours)*((60 pages)/(1 hour))          [hours cancel]

       (3 hours)*((60 pages)/(1 hour))*((80 words)/(1 page))

       (3)*(60)*(80) words

        14,400 words