Question 734376
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if {{{highlight(cross(a))}}} <U>it</U> takes an old sweeper 30 hour to clean a street and takes a new and old sweepers together 
only 7.5 hours to clean the same street, then how long would it take for new sweeper 
to {{{highlight(cross(cleanse))}}} <U>clean</U> the same street?
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<pre>
From the problem, the combined rate of the old and the new sweepers is  {{{1/7.5}}}  of the job
per hour, when they work together,

while the rate of the old sweeper is  {{{1/30}}}  of the job per hour.


So, the rate of the new sweeper, when it works alone, is the difference

    {{{1/7.5}}} - {{{1/30}}} = {{{(30-7.5)/(7.5*30)}}} = {{{21.5/(7.5*30)}}} = {{{3/30}}} = {{{1/10}}}

of the job per hour.


Hence, it will take 10 hours for the new sweeper to clean the street working alone.    <U>ANSWER</U>
</pre>

Solved.


This method analyzing rate of work via fractions is very powerful and effective way solving such problems.