A student is awake k hours each day and spend k/5 hours each day doing homework. In terms of k, how many days will it take the student to complete homework assignments that require a total of 20 hours?

number of days = 20 hrs / (k/5 hrs/day)

= 20(5/k) days
= 100/k days

testing:
suppose k = 10
is my answer reasonable?
Student would spend 10 hrs a day awake, ok
student would spend 2 hrs a day doing hmwk, ok
so to do a 20 hrs assignment should take 10 days
my formula 100/10 = 10 , ok!!!!

To find the number of days it will take the student to complete the homework assignments, we need to determine how many hours the student can complete in one day.

Since the student is awake for k hours each day and spends k/5 hours doing homework, the remaining hours he has available for homework each day is k - k/5 = 4k/5.

We can set up an equation to find the number of days it will take to complete 20 hours of homework:
(4k/5) * d = 20

To solve for d (the number of days), we divide both sides of the equation by 4k/5:
d = 20 / (4k/5)
d = (20 * 5) / 4k
d = (100 / 4k)

Therefore, it will take the student (100 / 4k) days to complete the homework assignments that require a total of 20 hours, in terms of k.

To find out how many days it will take the student to complete the homework assignments, we need to first determine how many hours the student spends on homework each day. According to the given information, the student spends k/5 hours on homework each day.

Next, we can calculate how many days it will take to complete the 20 hours of homework. To do this, we divide the total number of hours required by the number of hours the student spends on homework each day:

Number of days = Total hours required / Hours spent on homework each day

Number of days = 20 / (k/5)

To simplify this expression, we can multiply the numerator and denominator by 5:

Number of days = 20 * (5/k)

Simplifying further, we get:

Number of days = 100/k

Therefore, in terms of k, it will take the student 100/k days to complete the homework assignments that require a total of 20 hours.