   SEARCH HOME Math Central Quandaries & Queries  Question from Kenneth: Here is my question: 15 workers can finish a job in 7 days. If I want to find the number of days 21 workers can finish the job, the calculation becomes 1/(21 workers) X 15 workers X 7 days. If the 21 and 15 are reduced to 7 and 5, by dividing 21 and 15 by 3, the calculation becomes 1/7 X 5 X 7 days, what do these two reduced terms (7 and 5) indicate or represent? Do they represent 5 workers and 7 workers, as in (1/7 worker) X 5 workers X 7 days = 5 days? I thank you for your reply. Hi Kenneth,

I just try to use reasoning rather than a formula to approach this type of problem.

If 15 workers can finish a job in 7 days then a fifth as many workers will take five times as long. Thus if

15 workers can finish a job in 7 days

then

$\frac{15}{5} = 3$ workers can finish a job in $7 \times 5 = 35$ days.

Now if you have seven times as many workers it should only take one seventh the time. That is

$3 \times 7 = 21$ workers can finish a job in $\frac{35}{7} = 5$ days.

Does this help?

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.