Work Problems

In work problems, we are dealing with the rate of work, meaning how fast a person can finish a certain work. Equations in work problems mostly consist of fractions. Take note of what is being asked in the problem and use only one variable to avoid confusions. The answers are usually fractions but it is better to convert it into mixed fractions.

o Example

Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours. How long would it take the two painters together to paint the house?

The rate of one painter- 1/12

The rate of second painter- 1/8

multiples

( )( )

(12 (12

(12 (12

( (12

8t 96

20t 96

t or

First is to determine the rate of work. Rates are always in fraction form with the work on the numerator and the time in the denominator. In this problem, there’s only 1 work which is painting the house

Next is to set up the equation. In the problem, we are being asked to find the how long it will take to paint the house if the two painters work together. So we add the rate of the two painters. The variable we are using is t.

In solving equations like this, it is easier not to get the LCD but instead getting the multiples and multiplying them to the equation. The multiples are just the denominators of the rates so 12, 8 and t are the multiples.

The two painters can finish the

painting the house in or

hours.