Algebra Word Problems

Question

Working together Julio and Krystal can pick forty bushels of apples in 5.83 hours. Had she done it alone it would have taken Krystal 10 hours. Find how long it would take Julio to do it alone.

How do I set this up... I know the answer is 13.98, but how do I set it up???

Answer 1

Hi Sarah,

 

The key to solving work problems is to find out what part of a whole job each person contributes when doing the job together.

 

Julio's portion of the completed job can be expressed by this ratio:

    5.83 / x (hrs. worked together / hrs. worked alone)

 

Julio's portion of the completed job can be expressed by this ratio:
   5.83 / 10 (hrs. worked together / hrs. worked alone)

 

Adding these portions together to equal 1 whole completed job gives us our equation, which we can then use to solve for our unknown (x):

    (5.83 / x) + (5.83 / 10) = 1

 

   (10x)(5.83 / x) + 10x(5.83 / 10) = (10x)(1)

   58.3 + 5.83x = 10x

   10x - 5.83x = 58.3

           4.17x = 58.3

                 x = 58.3 / 4.17

                 x = 13.98 (Julio's hours to complete

                                        the job alone)

 

In work problems, the principle to always remember is that the sum of the individual work portions is equal to one completed task.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.