# Bar Model Method for a Job Problem – A Bi-model Approach

##### Ho Soo Thong

**Abstract**

This article illustrates the use of related bar models of two mathematical quantities for a visual view of a counting approach to a complex job problem.

Arithmetic of fractions has been used in the traditional approach to solve job problems in schools. A counting approach in the Bar Model Method was recently illustrated in [1].

In this article, we will illustrate a bi-model approach to a complex job problem at Primary Olympiad level.

**Problem**

Some workers are to work at two sites, A and B. The amount of work at site A and the amount of work at site B is in the ratio 3 : 2.

They began work in a morning, 60% of the workers are at site A and the rest of workers are at site B. In the afternoon the number of workers at site A is half of those at site B. The work at site B is done at the end of the day.

Next morning, 20 workers finished the remaining work at site A.

What is the total number of workers?

**Solution**

Noting that 60% = 3/5 , Figure 1 shows a comparison bar model for the distribution of numbers of workers.

Next, we let

*a morning job of a worker = an afternoon job of a worker = 1 unit of job*

In Figure 2, we refer to the distribution of workers in Figure 1 and construct bar models for work done at sites *A* and *B*.

A *fraction* bar model is added to depict the ratio 3 : 2.

Total number of workers = 3*b* = 30.

References

[1] Ho Soo Thong,* Bar Model Method for Job Problems*, AceMath 2013

[2] 朱华伟, 小学数学培优竞赛,中国少年儿童出版社2011

[3] 严军,小学数学奥赛优化解題,吉林教育出版社2007