<PRE><B>Question 975770</B>
&lt;br&gt;
Tutor @ikleyn has provided a solution using the standard formal method, using the rates of each worker.&lt;br&gt;
Here is a solution by a different method that can usually be used to solve these &quot;working together&quot; problems.&lt;br&gt;
Consider the least common multiple of the three given times needed for the three different pairs of workers to complete the job.  That least common multiple is 30 days.&lt;br&gt;
In 30 days...&lt;br&gt;
(1) A and B together can do the job 30/6 = 5 times;
(2) B and C together can do the job 30/10 = 3 times; and
(3) A and C together can do the job 30/7.5 = 4 times&lt;br&gt;
(4) From (2) and (3), A in 30 days can do the job 1 more time than B.&lt;br&gt;
(5) Then, from (1) and (4), in 30 days A can do the job 3 times and B can do it 2 times.&lt;br&gt;
Finally, from (5) and either (2) or (3), in 30 hours C can do the job 1 time.&lt;br&gt;
ANSWER: 30 hours&lt;br&gt;
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