Find what fraction of time was each step of the work. Then, write a ratio for the work done in each step considering what fraction of time was spent doing so.
11 13 hours
Practice makes perfect
Let's begin by making sense of the given information. We are told that one day Sumi and her apprentice work together for 2 hours and 16 minutes. Then, Sumi keeps working alone for an additional 4 hours and 32 minutes. Let's use a conversion factor to write the minutes as hours.
Next, we will find the total time spent on this work.
34/15+ 68/15= 102/15
We can find what fraction of time was each step of the work by dividing by this time. Let's find what fraction of time they worked together!
In a similar way, we can find what fraction of time Sumi worked alone.
Time
Time/Total Time
Fraction of Time
Working Together
34/15
3415/10215
1/3
Sumi Alone
68/15
6815/10515
2/3
We are told that Sumi can wash the windows from a building in 34 the time it takes her apprentice. Let t be the time it takes her apprentice to wash all the windows. We can write an expression for the time it takes each person if working individually.
Sumi:& 3/4t
Apprentice:& t
We can now write a ratio for the fraction of the work done in each part of the work.
Ratio
Fraction of Time
Fraction of Work
Working Together
1/t+1/34t
1/3
1/3( 1/t+1/34t)
Sumi Alone
1/34t
2/3
2/3( 1/34t)
Since the whole work was done in 10215 hours, we can write an equation for t by adding each fraction of the work done.
1/3 ( 1/t+1/34t ) + 2/3 ( 1/34t ) =1/10215
Let's solve this equation!
