<PRE><B>Question 250438</B>
&lt;br&gt;Rate-of-work-word-problems/250438 (2009-12-15 21:54:41): one roofer can put a new roof on a house three times faster than another. Working together, they can roof a house in 4 days. How long would it take the faster roofer working alone?&lt;br&gt;

Let x be the fastest roofers time to roof the house&lt;br&gt;

Then the slower roofers time will be 3x&lt;br&gt;

Use the following formula to calculate how the work is done:&lt;br&gt;

{{{1/A+1/B=1/C}}} where A &amp; B are the times done by themselves, and C is the time it takes them to do the work together, thus we have:&lt;br&gt;

{{{1/x+1/3x=1/4}}}&lt;br&gt;

{{{3/3x+1/3x+1/4}}}&lt;br&gt;

{{{4/3x=1/4}}}&lt;br&gt;

{{{3x=16}}}&lt;br&gt;

{{{x=16/3}}}&lt;br&gt;

So the fast roofer can do it by himself in about 5.33 days!  Hope that helps!  :)&lt;br&gt;</PRE>