Question

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

Answer 1

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 `k`.

That means,

`d = k/(m+w)`

Subbing in the values from the first bit of information:

`16 = k/(5)`

`k = 80`

So, `d = 80/(m+w)`

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

`d = 80/(4+6)`

`d = 8`

Answer 2

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;

`n = "Total Workers"`

`m = "Total Number of Days"`

Then we have;

`n -> m = n_1m_1 = n_2m_2`

Where;

`n_1 = 2 + 3 = 5`

`n_2 = 4 + 6 = 10`

`m_1 = 16`

`m_2 = ?`

Therefore;

`5 xx 16 = 10 xx m_2`

`80 = 10m_2`

Divide both sides by `10`

`(10m_2)/10 = 80/10`

`(cancel10m_2)/cancel10 = 80/10`

`m_2 = 80/10`

`m_2 = 8`

So it will take `8` days for `10` workers..

Hope this helps!

Answer 3

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

Explanation:

`color(blue)("Shorter technique")`
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.

`16/2=8" days"`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Much deeper look at the problem showing a useful technique.")`

Let the work rate for a man be `w_m`
Let the work rate for a woman be `w_w`

Let time in days be `t_d`

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

Then we have

`2w_mt_d+3w_wt_d=W_T`

Factoring out the time

`t_d(2w_m+3w_w)=W_T`

Set `2w_m+3w_w` as `x` giving

`xt_d=W_T`
~~~~~~~~~~~~~~~~~~~~~~~~~
Initial condition is that `t_d=16" days"`

Not that `xt_d=W_T` where `W_T` is a constant. So if `x` changes then `t_d` must also change in such a way that we still get `W_T`.

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 `x` we have `2x`
However as we have changed `xt_d` to `2xt_d` it will no longer equal `W_T`.

The thing is that the total amount of work needed( `W_T` )to complete the task will not change. It is constant.

So if `W_T` is fixed we must change `2xt_d` is such a way that it changes back to `xt_d`. We can do that by including the correction of `xx1/2`

So we end up with `2x xxt_d/2=W_t`

In other words we changed `xt_d` one way then changed it back again.

We know that `t_d=16" days"` so `t_d/2=16/2=8" days"`