<PRE><B>Question 1146303</B>
&lt;br&gt;
Here is an alternative to the standard method shown by the other tutor for solving &quot;working together&quot; problems.  Many students like this method because it avoids working with those fractions.&lt;br&gt;
Assume it is sensible for the &quot;job&quot; to be done multiple times; then consider the least common multiple of the given times.  The LCM of 10, 12, and 15 is 60.  So how many of these jobs can each combination of boys do in 60 days?&lt;br&gt;
Joseph and Bill in 60 days can do 60/10 = 6 of these jobs.
Bill and Elmer in 60 days can do 60/12 = 5 of these jobs.
Elmer and Joseph in 60 days can do 60/15 = 4 of these jobs.&lt;br&gt;
So write equations for the numbers of jobs each combination of boys can do in 60 days:&lt;br&gt;
(1) J+B = 6
(2) B+E = 5
(3) E+J = 4&lt;br&gt;
Add the three equations and simplify:&lt;br&gt;
(4) J+B+E = 7.5&lt;br&gt;
Now compare (4) with each of (1), (2), and (3):&lt;br&gt;
E = 7.5-6 = 1.5
J = 7.5-5 = 2.5
B = 7.5-4 = 3.5&lt;br&gt;
Elmer alone can do 1.5 of these jobs is 60 days; so working alone he can complete one job in 60/1.5 = 40 days.&lt;br&gt;
Joseph alone can do 2.5 of these jobs in 60 days; so working alone he can complete one job in 60/2.5 = 24 days.&lt;br&gt;
Bill alone can do 3.5 of these jobs in 60 days; so working alone he can complete  one job in 60/3.5 = 120/7 = 17 1/7 days.&lt;br&gt;
ANSWERS:
Elmer: 40 days
Joseph: 24 days
Bill: 17 1/7 days</PRE>