Question 1125204
Say it like this:


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Eight workers, each working at the same rate, can finish a quantity of work in 16 days.  After working for 4 days,2 workers felt sick and never returned back.  How many days did the the remaining workers take to complete the work?
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r, the rate of 1 worker
{{{8r*16=1}}}, using "a quantity of work" as 1 whole piece of work.



The two separate numbers of workers for different time quantities, x for the unknown time quantity:
{{{8r*4+6r*x=1, completing the work with the 6 remaining workers}}}

{{{6rx=1-42r}}}
{{{6(1/(8*16))x=1-32(1/(8*16))}}}
{{{(3/(64))x=1-1/4}}}

{{{x=(1-1/4)(64/3)}}}

{{{x=(3/4)(64/3)}}}

{{{x=64/4}}}

x=16

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A different try:

After the full eight worked for 4 days,  {{{3/4}}} of the job still needed to be done.  That is, 6 workers must work for x days to complete {{{3/4}}} of the job.

{{{6r*x=3/4}}}

{{{x=(3/4)(1/6)(1/r)}}}

{{{x=(1/8)(1/r)}}}

{{{x=(1/8)(8*16)}}}

{{{highlight(x=16)}}}


16 more days