Sumi can wash the windows in 3/4 the time it takes her apprentice. One day they worked together for 2h 16 min, and then sumi continued alone. It took her 4h 32 min more to complete the job. How long would it take her apprentice to wash all the windows alone?
Let's denote by "x" the time it takes the apprentice to wash all the windows alone.
So, Sumi takes (3/4)x to wash all the windows alone.
Working together for 2 hours and 16 minutes is equal to (2 hours) + (16 minutes)/60 = 2.27 hours.
During this time, they complete the fraction (2.27)/(3/4) = (2.27)/(3/4) = (2.27)(4/3) = 3.03.
After working together, Sumi takes an additional 4 hours and 32 minutes to complete the job, which is equal to (4 hours) + (32 minutes)/60 = 4.53 hours.
Therefore, Sumi took a total of 2.27 hours + 4.53 hours = 6.8 hours to complete the job alone.
This is equivalent to 6 hours and 48 minutes.
So, her apprentice takes x hours to clean all the windows alone, and Sumi takes 6 hours and 48 minutes to clean all the windows alone.
Thus, we have the equation:
x = 6 hours + 48 minutes)/60
x = (6/1) + (48/60) = 6.8 hours
This means that the apprentice takes 6.8 hours to wash all the windows alone.