Word problem

Question

Working with your cousin you can refinish a table in 3 hours. Working alone your cousin can complete the job in four hours. How long would it take you to refinish the table working alone?

Answer 1

Hi Tiffany,

 

Let's begin by writing an equation in words to express the sum of each person's part in completing 1 whole job:

    Cousin's Part + Your Part = 1 (Whole Job)

 

Now let's write a mathematical expression to represent each person's part of the completed job:

    Cousin's Part = (3 hrs)(1 / 4 hrs)

    Your Part = (3 hrs)(1 / x hrs)

 

Each person's part is the ratio of each person's rate of work per hour times the 3 hours of working together.

 

Now let's write our equation using our mathematical expressions and solve it for our unknown (x) - the number of hours for you to complete the job alone:

    3(1/4) + 3(1/x) = 1

    3/4 + 3/x = 1

    4x(3/4) + 4x(3/x) = 4x(1)

    3x + 12 = 4x

    4x - 3x = 12

            x = 12 (number of hours for you to
                            complete the job alone)

 

We can check our answer by plugging it back into our equation and see if the fractions add up to 1:

    3/4 + 3/x = 1

    3/4 + 3/12 = 1

    (3 x 3)/(4 x 3) + 3/12 = 1

    9/12 + 3/12 = 1

    12/12 = 1

    1 = 1 (fractions add up to 1)

 

Since the sum of our fractions concerning each person's portion of the completed job do add up to 1 whole job, we are confident that our answer is correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.