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?
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'
Let's first convert the given time values to minutes for easier calculations.
2 hours and 16 minutes can be written as 2*60 + 16 = 136 minutes.
4 hours and 32 minutes can be written as 4*60 + 32 = 272 minutes.
Let's assume that the apprentice takes x minutes to wash all the windows alone.
In 136 minutes, both Sumi and the apprentice worked together.
So, the portion of work done by Sumi in 136 minutes = 3/4.
The portion of work done by the apprentice in 136 minutes = 1 - 3/4 = 1/4.
Now, we can set up the equation:
136/x = 3/4.
Cross-multiplying the equation, we get:
136 * 4 = 3 * x.
Simplifying the equation, we have:
544 = 3x.
Dividing both sides by 3, we get:
x = 544/3 = 181.33.
Therefore, it would take the apprentice approximately 181.33 minutes to wash all the windows.
To find out how long it would take Sumi's apprentice to wash all the windows, we need to break down the information given into smaller steps.
Let's assign variables to the unknown quantities. Let x represent the time it takes Sumi's apprentice to wash all the windows. Since Sumi can wash the windows in 3/4 the time it takes her apprentice, Sumi's time can be represented as (3/4)x.
Now, let's use the given information. It is mentioned that Sumi and her apprentice worked together for 2 hours and 16 minutes, which is equivalent to 2 + 16/60 = 2.27 hours.
During this time, they completed a part of the job together. This part of the job can be represented as (1/2.27) (since their combined work rate is 1/2.27 of the job per hour). Therefore, the remaining part of the job for Sumi to complete alone is (1 - 1/2.27).
We know that Sumi took an additional 4 hours and 32 minutes to finish the job alone, which is equivalent to 4 + 32/60 = 4.53 hours.
Now, we can set up an equation to solve for x:
[(1 - 1/2.27) * x] = 4.53
To solve this equation, we can multiply both sides by 2.27 to remove the fraction:
x - (1/2.27) * x = 4.53 * 2.27
x - (1/2.27) * x = 10.2961
Next, we simplify the equation:
(2.27 - 1)x = 10.2961
1.27x = 10.2961
Finally, we solve for x:
x = 10.2961 / 1.27
x ≈ 8.11
Therefore, it would take Sumi's apprentice approximately 8.11 hours (or 8 hours and 6 minutes) to wash all the windows.