Algebra word problem

Question

Julie wraps bacon around deep-fried shrimp at a rate of x shrimps per hour. Samantha wraps shrimp twice as fast as Julie. In terms of x and y, how many more hours will it take Julie to wrap y shrimp?

Answer 1

 

Setup a proportion for Julie

 

     x shrimp       y shrimp

    ---------------- = -------------

      1 hour          h hours

 

    cross multiply

 

    xh = y

 

     h = y/x

 

    Julie can wrap y shrimp in y/x hours

 

Set up a proportion for Samantha ... she works twice as fast, so she can do 2x shrimp in an hour

 

     2x shrimp          y shrimp

    ------------------ = ---------------

        1 hr                h hours

 

    Cross multiply

 

    2xh = y

 

      h = y/2x

 

The difference between the 2 expressions represents the difference in amount of shrimp wrapped

 

       y         y

     -----  -  ----

       x        2x

 

      2y         y

=  -----  -  -----

      2x        2x

 

     2y - y

= ----------

       2x

 

     y

= ----

    2x