integers question?

Question

hi everyone,
can someone please help me on this integers question and show me in steps how to do it so i understand? thanx!

Find all the possible values for the whole positive number 'n' so that -6 / n-6 is also a whole positive number.

thanks!

p.s. there is something i want to double check with all the smart people out there..lol

a train takes 40 mins to travel 24km to the city. what is its average speed?
will the answer be 36km/h?

thanx in advance...

Answer 1

for -6/n-6 to be a integer 6 should be divisible by n-6 or
6=k(n-6) such that k is a negative integer
so possible values are
k=-1, n-6=-6 n=0
k=-2, n-6=-3 n=3
k=-3, n-6=-2 n=4
k=-6, n-6=-1 n=5

As for the 2nd one, well I am not that smart but I think that 36 should be correct.

Answer 2

Part a.

n = 0. -6/ n - 6 = -6/ 0 - 6 = -6/ -6 = 1
n = 3. -6/ n - 6 = -6/ 3 - 6 = -6/ -3 = 2
n = 4. -6/ n - 6 = -6/ 4 - 6 = -6/ -2 = 3
n = 5. -6/ n - 6 = -6/ 5 - 6 = -6/ -1 = 6
n = 6. -6/ n - 6 = -6/ 6 - 6 = -6/ 0 = ?

Part b.

40min = 2/3 hr.
Speed = Distance / time.
Speed = 24km / 2/3hr
Speed = [24 * 3/2] / hr
Speed = 36km/ hr.

Answer 3

Your answer to the train question is correct.
n = 3 gives -6/(n - 6) = -6/-3 =2
n = 5 gives -6/(n - 6) = -6/-1 = 6
n = 0 will give a positive integer but this is disallowed because you said that n had to be positive.
I don't think that there is any way to do it other than trying numbers and seeing which works.