If it takes one person 4 hours to paint a room and another person 12 hours to paint the same room, working together they could paint the room even quicker, it turns out they would paint the room in 3 hours together. This can be reasoned by the following logic, if the first person paints the room in 4 hours, she paints 14 of the room each hour. If the second person takes 12 hours to paint the room, he paints 1 of the room each hour. So together, each hour they paint 1 + 1 of the 12 4 12 room. Using a common denominator of 12 gives: 3 + 1 = 4 = 1. This means 12 12 12 3 each hour, working together they complete 13 of the room. If 13 is completed each hour, it follows that it will take 3 hours to complete the entire room. This pattern is used to solve teamwork problems. If the first person does a job in A, a second person does a job in B, and together they can do a job in T (total). We can use the team work equation. Teamwork Equation: A1 + B1 = T1 Often these problems will involve fractions. Rather than thinking of the first frac- tion as A1 , it may be better to think of it as the reciprocal of A’s time. World View Note: When the Egyptians, who were the first to work with frac- tions, wrote fractions, they were all unit fractions (numerator of one). They only used these type of fractions for about 2000 years! Some believe that this cumber- some style of using fractions was used for so long out of tradition, others believe the Egyptians had a way of thinking about and working with fractions that has been completely lost in history.
