# Algebra

Sumi can wash the windows of an office building in 3/4 the time it takes her apprentice. One day they worked on the building together for 2h 16min , then Sumi continued to work alone. It took 4h 32min more to complete the job. How long would it take her apprentice to wash all the windows?

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1. 2h16' = 34/15 hours
4h32' = 68/15 hours

Suppose it takes t hours to do the job working together. If the apprentice takes x hours, then it takes Sumi 3/4 x hours. So, we know that

1/t = 1/x + 1/(3/4 x)

Also, we are told that

(34/15)(1/t) + (68/15)(1/(3/4 x)) = 1

solving those equations together, we get

x = 34/3 = 11h20'

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posted by Steve

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