<p>Can someone please help me with these problems? I'll keep updating this post / thread with problems I've finding difficulty with. </p>
<p>John can complete a job in 12 the time it
takes Harry to complete the same job. If they both work together they can
complete the job in 4 hours. How long does it take John to do the job alone?</p>
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<p>Harry takes 6 hours.
John takes 3 hours.</p>
<p>3j = 60
j = 20/hr</p>
<p>6h = 60
h = 10/hr</p>
<p>j+h = 30/hr</p>
<p>If they have 120 hrs of labor total (assuming their efficiency is 30/hr), then John would complete the job in 6 hours by himself.</p>
<p>I know there’s an algebraic solution, but this should be correct.</p>
<p>I beleive the correct answer is 1.5 hours, Let H equal the amount of time it take Harry to do the job. And from the I question(its missing a few words), I am assuming it is saying John can complete the job in a 12th of the time it took Harry so that value will equal H/2. Rate is 1/Time. Rate of Harry is 1/H and rate of John is 2/H. There is an equation [2(RateX)(RateY)]/(Rate X + Rate Y)=4. Thats the equation you use when finding combined time. Plug in the value solve for H. Which I got as 1/3. So The amount of time it takes John to the job is 3/2 which is equal to 1.5 hours.</p>
<p>Each person does x and y jobs per hour, respectively. Together, they do a job in t hours. Therefore, t/x + t/y = 1.
Ta-da.</p>