Question 1205975
<br>
(1) The classic algebraic solution method (but presented informally)....<br>
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.<br>
(2) An alternative method, also presented informally....<br>
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.<br>
(3) The standard shortcut....<br>
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.<br>