math

The men work  7/3 times as fast as the women

To see this.....let each woman perform 1 unit of work per hour.....then, they complete 14 units of work per hour.......but it only takes 6 men to do the same amount of work per hour because 6 * (7/3)units of work per hour  =  42/3  = 14 units of work per hour.....

So......in  each 10 units ot work, the men do  7 of them and the women do 3 of them

Let's look at the portion of the job completed in one hour......there are 240 hours in 10 days = 240 hours.......so one hour represents 1/240  of the job

So...In one hour, the men complete  .7 of the work    and the women complete .3 of the work  done in that hour

So.......the portion of the job completed by the men in one hr  =  (7/10)(1/2400) =  7/2400 of the job

And the portion of the job completed by the womwen in one hour = (3/10) (1/2400) =  3/2400 of the job

So.......when the men are doubled.....they will be able to complete  14/2400 of the job in one hour and the women........since there is no increase in their number, complete the same amount of the job as before

So we have this equation

 [14/2400] t  +  [3/2400] t  =  1    where t is the time in hours to complete the job with the added men

[17 / 2400] t  = 1   ⇒  t = 2400/17  ≈  141.176 hrs ≈ 5.88 days