Solving a Problem about Work (2.3.2)

Question 1

• A linear work problem calculates work performed at an average rate over a period of time by one or more workers.

Answer 1

• A linear work problem calculates work performed at an average rate over a period of time by one or more workers.

Question 2

This type of problem asks that two rates be linked to complete usually one job.

The rates are set up in fractions with the number of hours
required to finish the job working alone as the denominator and the number of hours actually worked as the numerator.

Answer 2

This type of problem asks that two rates be linked to complete usually one job.

The rates are set up in fractions with the number of hours
required to finish the job working alone as the denominator and the number of hours actually worked as the numerator.

Question 3

Since the problem asks about time, define a variable, t, for time used.

Since Ms. B. could build the entire fence in 8 hours, set up a fraction:

t = time Ms. Burger will use
8 = hours used if Ms. Burger worked alone

Answer 3

Since the problem asks about time, define a variable, t, for time used.

Since Ms. B. could build the entire fence in 8 hours, set up a fraction:

t = time Ms. Burger will use
8 = hours used if Ms. Burger worked alone

Question 4

Next assign a variable, r, to represent Dr. Burger’s

fence-building speed. Then set up a fraction for his rate to match the fraction for his mother’s rate.

Answer 4

Next assign a variable, r, to represent Dr. Burger’s

fence-building speed. Then set up a fraction for his rate to match the fraction for his mother’s rate.

Question 5

As the last step, set up an equation for building the fence. Add the two fractions to get 1. The 1 represents one job completed; in this case, one fence built.

Answer 5

As the last step, set up an equation for building the fence. Add the two fractions to get 1. The 1 represents one job completed; in this case, one fence built.

Question 6

The problem states that if they build the fence together it will take five hours. So, t = 5.

Now solve the equation for r.
The value for r is Dr. Burger’s rate and that answers the
question that the problem posed.

Answer 6

The problem states that if they build the fence together it will take five hours. So, t = 5.

Now solve the equation for r.
The value for r is Dr. Burger’s rate and that answers the
question that the problem posed.