Question 1205975: Josh can clean the math building on his campus in 3 hours. Ken takes 7 hours to clean the same building. If they work together, how long will it take them to clean this building?
Found 4 solutions by greenestamps, mananth, josgarithmetic, math_tutor2020:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
(1) The classic algebraic solution method (but presented informally)....
John cleans 1/3 of the building in 1 hour
Ken cleans 1/7 of the building in 1 hour
Together the fraction of the building they clean in 1 hour is 1/3+1/7 = 7/21+3/21 = 10/21
So the number of hours it takes them to clean the building together is 21/10 hours.
(2) An alternative method, also presented informally....
Consider the least common multiple of the two times, which is 3*7 = 21 hours
In 21 hours, John could clean the building 21/3 = 7 times
In 21 hours, Ken could clean the building 21/7 = 3 times
So in 21 hours the two of them could clean the building 7+3 = 10 times
So the time it takes them to clean the building once is 21/10 hours.
(3) The standard shortcut....
If the two workers individually can do the job in A hours and B hours, then the number of hours it takes them to do the job together is (AB)/(A+B). In this problem, (7*3)/(7+3) = 21/10.
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website! Josh can clean the math building on his campus in 3 hours. Ken takes 7 hours to clean the same building. If they work together, how long will it take them to clean this building?
Josh can clean the math building on his campus in 3 hours
Assune cleaning the building as one job,
So josh can do 1/3 of the job in 1 hour.
Ken takes 7 hours to clean the same building.
So he does 1/7th of the job in 1 hour
If they work together they do (1/3 +1/7 ) of the job in 1 hour
= 10/21 of the job in 1 hour
Therefore to complete the job together they take 21/10 hours = 2.1 hours.
Answer by josgarithmetic(39617)  (Show Source):
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Consider the area to clean is 210 square feet.
I'm getting this value from the fact 7*3 = 21 is the LCM of the given values.
Then I tacked on a 0 at the end to make the square footage more realistic.
This is just an example value. Feel free to pick another.
Josh cleans 210 sq ft in 3 hours when working alone.
His unit rate is 210/3 = 70 sq ft per hour.
Ken cleans 210 sq ft in 7 hours when working alone.
His unit rate is 210/7 = 30 sq ft per hour.
Add the unit rates: 70+30 = 100
If the two men work together, without either person getting in the way of the other, then their combined unit rate is 100 sq ft per hour.
When working together it will take 210/100 = 2.1 hours.
If you wanted the answer in minutes only, then,
2.1 hrs = 2.1*60
2.1 hrs = 126 min
Or if you wanted hrs+min format,
126 min = 120 min + 6 min
126 min = 2 hr + 6 min
|
|
|
