Question 1204175
P can complete a task in x days while Q takes (x + 12) days to do the same task.
a) What fraction of the task can each of them complete in a day?<pre>
P can complete 1 task in x days, so P can complete 1/x of a task in 1 day.
Q can complete 1 task in (x + 12) days, so Q can complete 1/(x + 12) of a task
in 1 day.</pre>
b) If both of them work together, they can
complete the task in 8 days. Find x.<pre>
P can complete 1/x of a task in 1 day, so P can complete 8/x of a task in 8
days.
Q can complete 1/(x + 12) of a task in 1 day, so Q can complete 8/(x + 12) of a
task in 8 days.
So together, they can complete 8/x + 8/(x+12) of a task in 8 days

That's 1 task, so 

{{{8/x+8/(x+12)}}}{{{""=""}}}{{{1}}}

LCD = x(x + 12)

{{{8(x+12) + 8x}}}{{{""=""}}}{{{x(x+12)}}}

{{{8x+96+8x}}}{{{""=""}}}{{{x^2+12x}}}

{{{16x+96}}}{{{""=""}}}{{{x^2+12x}}}

{{{x^2+12x}}}{{{""=""}}}{{{16x+96}}}

{{{x^2-4x-96}}}{{{""=""}}}{{{0}}}

{{{(x+8)(x-12)}}}{{{""=""}}}{{{0}}}

x+8=0; x-12=0
  x=-8;   x=12

x cannot be negative.

x = 12.

Now that we have x, we can answer (a) as a numerical fraction:

a) What fraction of the task can each of them complete in a day?<pre>
P can complete 1 task in 12 days, so P can complete 1/12 of a task in 1 day.
Q can complete 1 task in (12 + 12) = 24 days, so Q can complete 1/(12 + 12) = 1/24 of a task in 1 day.</pre>Edwin</pre>