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
Dec 14, 2017

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

Dec 14, 2017

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!

Dec 14, 2017

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"