A Town's Old Street Sweeper Can Clean The Streets In 60 H. The Old Sweeper Together With A New Sweeper Can Clean The Streets In 15 H. How Long Would It Take The New Sweeper To Do The Job Alone?
Answer:
Let S be the time required by the new street sweeper.
1/(60 h) + 1/S = 1/(15 hr) (total the number of "streets/hr")
S + 60 hr = 4S (multiply the equation by 60S hr, the least common denominator)
60 hr = 3S (subtract S from both sides)
20 hr = S (divide both sides by 3)
The bright sweeper can do the job alone in 20 hours.
_____
We could solve this by subtracting 1/(60 hr) from both sides
1/S = 1/(15 hr) - 1/(60 hr) = 4/(60 hr) - 1/(60 hr) = 3/(60 hr)
1/S = 1/(20 hr)
S = 20 hr (take the reciprocal of both sides)
I think 20hrs
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