Week 314 (15th September 2023)

Raj works as a Financial Controller in an office based in Birmingham.   

The building that she works in requires some essential maintenance work. 

15 workers can complete the required maintenance work in 8 days. However, Raj’s boss would like the work completed quicker! 

How many more workers are needed to complete the job in 6 days? 

Assume that all of the workers work at the same rate.   


The number of days of maintenance work is inversely proportional to the number of workers. This is because as the number of workers increases, the number of days it takes to complete decreases.  

Days = k / number of workers

Where k is a whole number constant.  

Now we can substitute in our values to work out the constant k.  

8 = k/15 

k = 8 x 15 = 120  

If we use the value for k and our target of 6 days, we can find out how many workers are needed.   

6 = 120/workers  

workers = 120/6 = 20 workers needed.   

If we already have 15 workers, then 5 extras are needed for the work to be completed in 6 days.