SOLUTION: shabbir can paint a shed in 5 hours working alone, whereas rehan can paint it in 6 hours.they start together. but rehan had to leave after 2 hours to do his homework. how long did

Question 468847: shabbir can paint a shed in 5 hours working alone, whereas rehan can paint it in 6 hours.they start together. but rehan had to leave after 2 hours to do his homework. how long did it take shabbir ti complete painting the shed alone?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
rate * time = units of work.
unit of work is 1 shed.
shabbir does it in 5 hours working alone.
shabbir's formula is:
rate * 5 = 1
shabbir's rate of work is 1/5 of the shed in 1 hour.
rehan does it in 6 hours working alone.
rehan's formula is:
rate * 6 = 1
rehan's rate of work is 1/6 of the shed in 1 hour.
they work together for 2 hours.
their combined rate of work is (1/5 + 1/6) per hour.
this is equivalent to a combined rate of 11/30 per hour.
since rate * time = units of work, they complete:
11/30 * 2 = 22/30 units of work in 2 hours.
since the total job is 1 unit of work, 8/30 unit of work remain.
shabbir has to finish the job.
the formula is still rate * time = units of work.
replace rate with shabbir's rate and replace units of work with 8/30 and you get:
1/5 * time = 8/30
divide both sides of this equation by (1/5) to get
time = (8/30) / (1/5) = 40/30 hours.
it will take shabbir an additional 40/30 hours to finish the job.
they worked for 2 hours together and their combined rate of work is 11/30 so they completed 22/30 of the job in 2 hours.
shabbir worked for 40/30 hours and his rate of work is 1/5 per hour so he completed (40/30) * (1/5) = (40/150) of the job working alone.
(40/150) is equivalent to (8/30).
shabbir and rehan completed 22/30 of the job working together and then shabbir finished the rest of it working alone, which was 8/30 of the job.
the total time they took to finish the job is 2 hours plus 40/30 hours.
this is equal to 100/30 hours which is equal to 3 + 10/30 hours which is equal to 3 and 1/3 hours which is equal to 3 hours and 20 minutes.
the decimal equivalent is 3.3333333333 hours.

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