Question 831418
<pre>
Check the problem again. A piece of information is missing.  
There are 5 unknowns, but there is only enough information 
to get 4 equations.  That's called an "underdetermined" system.
(I'm assuming you're not taking linear algebra, or are you?
I'll assume you aren't.)  We can at best get some of times, 
and we may not get any! But let's see how far we can get
without the missing piece of information.

Let The answers be:
It takes A "a" hours to complete the task alone.
It takes B "b" hours to complete the task alone.
It takes C "c" hours to complete the task alone.
It takes D "d" hours to complete the task alone.
It takes E "e" hours to complete the task alone.

Then 
A's working rate is 1 task per "a" hours or {{{1/a}}} tasks/hour
B's working rate is 1 task per "b" hours or {{{1/b}}} tasks/hour
C's working rate is 1 task per "c" hours or {{{1/c}}} tasks/hour
D's working rate is 1 task per "d" hours or {{{1/d}}} tasks/hour
E's working rate is 1 task per "e" hours or {{{1/e}}} tasks/hour
</pre>a unit of tasks can be completed by A, B, C, D and E in 2 hours.<pre>
So their combined working rate is  1 task per "2" hours or {{{1/2}}} tasks/hour

{{{(matrix(3,1,"A's",working,rate))}}}{{{""+""}}}{{{(matrix(3,1,"B's",working,rate))}}}{{{""+""}}}{{{(matrix(3,1,"C's",working,rate))}}}{{{""+""}}}{{{(matrix(3,1,"D's",working,rate))}}}{{{""+""}}}{{{(matrix(3,1,"E's",working,rate))}}} {{{""=""}}} {{{(matrix(4,1,their, combined, working,rate))}}}

So

{{{1/a}}}{{{""+""}}}{{{1/b}}}{{{""+""}}}{{{1/c}}}{{{""+""}}}{{{1/d}}}{{{""+""}}}{{{1/e}}} {{{""=""}}} {{{1/2}}}</pre>If it is done by A and B, it can be completed in 4 hours 48 minutes,<pre>
4 hours and 48 minutes is {{{4+48/60}}} = {{{4+4/5}}} = {{{14/5}}}

So their combined working rate is 1 task per {{{14/5}}} hours or {{{1/(14/5)}}} or {{{5/14}}} tasks/hour

{{{(matrix(3,1,"A's",working,rate))}}}{{{""+""}}}{{{(matrix(3,1,"B's",working,rate))}}} {{{""=""}}} {{{(matrix(4,1,their, combined, working,rate))}}}

{{{1/a}}}{{{""+""}}}{{{1/b}}} {{{""=""}}} {{{5/14}}}</pre>by B, C and D in 4 hours,<pre>So their combined working rate is 1 task per 4 hours or {{{1/4}}} tasks/hour.

{{{(matrix(3,1,"B's",working,rate))}}}{{{""+""}}}{{{(matrix(3,1,"C's",working,rate))}}}{{{""+""}}}{{{(matrix(3,1,"D's",working,rate))}}} {{{""=""}}} {{{(matrix(4,1,their, combined, working,rate))}}}

{{{1/b}}}{{{""+""}}}{{{1/c}}}{{{""+""}}}{{{1/d}}} {{{""=""}}} {{{1/4}}}</pre>and by A, C and E in 3 hours 12 minutes.<pre>3 hours and 12 minutes is {{{3+12/60}}} = {{{3+1/5}}} = {{{16/5}}}

So their combined working rate is 1 task per {{{16/5}}} hours or {{{1/(16/5)}}} or {{{5/16}}} tasks/hour

{{{(matrix(3,1,"A's",working,rate))}}}{{{""+""}}}{{{(matrix(3,1,"C's",working,rate))}}}{{{""+""}}}{{{(matrix(3,1,"E's",working,rate))}}}{{{""=""}}} {{{(matrix(4,1,their, combined, working,rate))}}}

{{{1/a}}}{{{""+""}}}{{{1/c}}}{{{""+""}}}{{{1/e}}} {{{""=""}}} {{{5/16}}}

So we have the system of 4 equations in 5 unknowns;  

{{{system(1/a+1/b+1/c+1/d+1/e=1/2,
1/a+1/b=5/14,1/b+1/c+1/d=1/4,1/a+1/c+1/e=5/16)}}}

We consider the reciprocals to be the variables and
make this 4×6 augmented matrix:

{{{(matrix(4,7,

1,1,1,1,1,"|",1/2,
1,1,0,0,0,"|",5/14,
0,1,1,1,0,"|",1/4,
1,0,1,0,1,"|",5/16))}}}

Using a TI graphing calculator I get the "rref":

{{{(matrix(4,7,

1,1,1,0,1,"|",1/4,
0,1,0,0,-1,"|",3/28,
0,0,1,0,0,"|",1/16,
0,0,0,1,1,"|",9/112))}}}

The third row translates as

{{{1/c=1/16}}}, so c=16 and it takes C 16 hours to complete the task

So we substitute c=16 in the system

{{{system(1/a+1/b+1/16+1/d+1/e=1/2,
1/a+1/b=5/14,1/b+1/16+1/d=1/4,1/a+1/16+1/e=5/16)}}}

and simplify

{{{system(1/a+1/b+1/d+1/e=7/16,
1/a+1/b=5/14,1/b+1/d=3/16,1/a+1/e=1/4)}}}

We'll put it in a 4×5 augmented matrix.  But I'm quite 
sure that will be a singular matrix.

{{{(matrix(4,6,

1,1,1,1,"|",7/16,
1,1,0,0,"|",5/14,
0,1,1,0,"|",3/16,
1,0,0,0,"|",1/4))}}}

And get the "rref"

{{{(matrix(4,6,

1,0,0,1,"|",1/4,
0,1,0,-1,"|",3/28,
0,0,1,1,"|",9/112,
0,0,0,0,"|",0))}}}

See? The bottom row is all 0's.

So the only answer we can get without the missing piece of
information is that C can complete the task in 16 hours.

Edwin</pre>