Question 734376
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An informal solution, using logical reasoning instead of the formal algebra shown in the response from the other tutor....<br>
When the new sweeper joins the old one, the job is completed in 1/4 as much time (7.5 hours instead of 30), so it is as if there are now 4 of the old sweepers working.<br>
That means the new sweeper does as much work as 3 of the old sweepers.<br>
And since the old sweeper can do the job alone in 30 hours, the new sweeper can do the job alone is 1/3 as much time, which his 10 hours.<br>
ANSWER: 10 hours<br>