Question 49436
Not a lot of algebra going on here, just some number sense. 
After 5 days, the students have completed one-third of the problems.  We don't know how many that is, nor do we care.  Now, on the next day, they must complete twice as many as they had done, which is twice of one-third, or the next two-thirds.  Therefore, on the sixth day, they complete the other two-thirds of the problems.  Which means all of the problems are done.  So it takes six days to complete all of the HW.