# 2 men and 3 women take 16 days to complete a task. How long would it take for 4 men and 6 woman?

##### 3 Answers

8 days

#### Explanation:

We know that the number of days is inversely proportional to the number of men and women, with respect to some constant

That means,

Subbing in the values from the first bit of information:

So,

Substituting the second bits of information into the formula, we get the equation:

Please see the steps and process in solving the question above..

#### Explanation:

In this kind of question, you should note that the higher the number of workers the lower the number of days..

So lets start solving..

Let;

Then we have;

Where;

Therefore;

Divide both sides by

So it will take

Hope this helps!

8 days. Full explanation given building the solution one step at a time.

#### Explanation:

If you double the work force they will put in double the amount of work. So the task will be completed twice as quickly. That is, you halve the time.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let the work rate for a man be

Let the work rate for a woman be

Let time in days be

Let the total amount of work needed to complete the task be

Then we have

Factoring out the time

Set

~~~~~~~~~~~~~~~~~~~~~~~~~

Initial condition is that

Not that

This is the same principle as that of measuring power used in your home verses time -> kilowatt hours.

Both the count of men and women have doubled

So instead of just

However as we have changed

The thing is that the total amount of work needed(

So if

So we end up with

In other words we changed

We know that