Question 734376
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There are many great answers by the other tutors.


Here's yet another approach.
Let's say the street length is 3000 feet in total. 
The value 3000 doesn't matter and can be changed to any other number you want, since the final answer at the end will be the same.


The old sweeper does the full job in 30 hours when working alone.
The old sweeper's rate is (3000 ft)/(30 hr) = 100 feet per hour.


The new sweeper takes x hours to do the job when working alone.
The new sweeper's rate is 3000/x feet per hour.


Their combined rate is 100 + (3000/x) feet per hour.
This assumes that neither sweeper hinders the other. 
Multiplying this combined rate by 7.5 hours should lead to the total 3000 feet needed to be cleaned.
7.5*( 100 + (3000/x) ) = 3000
which solves to <font color=red>x = 10</font>


Therefore the new sweeper needs <font color=red>10 hours</font> to clean the entire street by itself.
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