Question 1037379
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A and B working together can finish the job in 10 days. 
If A works 4 days and B works 3 days, one-third of the job shall be finished. 
How many days will it A to finish the job
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There is much easier and more straightforward way to solve the problem, if you correctly choose the unknowns.


<pre>
Let "a" be the rate-of-work of A, and
let "b" be the rate-of-work of B.

Then from the condition you immediately get these two equations for two unknowns

10a + 10b = 1,    (1)
 4a +  3b = {{{1/3}}}.   (2)

Multiply equation (2) by 3 (both sides). Then you can rewrite the system in the form

10a + 10b = 1,    (1')
12a +  9b = 1.    (2')

Now, multiply equation (1') by 6, multiply equation (2') by 5 and distract.
In this way you eliminate "a" and obtain a single equation for "b"

60b - 45b = 5 - 4,   or   15b = 1,   b = {{{1/15}}}.

Then from (1)  10a = 1 - 10b = 1 - {{{10/15}}} = 1 - {{{2/3}}} = {{{1/3}}},
Hence, a = {{{1/30}}}.
The rate of "a" is {{{1/30}}} job-per-day; the rate of "b" is {{{1/15}}} job-per-day.

<U>Answer</U>. A will complete the job in 30 days.  B will complete the job in 15 days.
</pre>

<U>The lesson to learn from this solution</U>:  choose correctly the unknowns when solving rate-of-work and joint-work problems.