SOLUTION: if a 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

Algebra ->  Rate-of-work-word-problems -> SOLUTION: if a 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       Log On


   

Question 734376: if a 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 cleanse the same street?
Found 2 solutions by lynnlo, josmiceli:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hours for new sweeper to clean street
The new sweeper's rate of sweeping is ( 1 street cleaned ) / ( t hrs )
The old sweeper's rate of sweeping is ( 1 street cleaned / 30 hrs )
Together, their rate is ( 1 street cleaned ) / ( 7.5 hrs )
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Add their rates of sweeping to get their rate sweeping together
+1+%2F+30+%2B+1+%2F+t+=+1%2F+7.5+
Multiply both sides by +30t+
+t+%2B+30+=+4t+
+3t+=+30+
+t+=+10+
It will take the new sweeper 10 hrs to clean street
check:
+1%2F30+%2B+3%2F30+=+4%2F30+
+4%2F30+=+4%2F30+
OK