Hi, I'm not sure if this is the right section for this question, so if not please redirect me to the correct subforum.
Q: There are k animal feeding stations arranged in a line with a supply hut. The stations are s yards apart and the nearest is t yards from the hut. An attendant carries n bags of feed, one at a time, to each feeding station. How far will he have traveled when he arrives back at the hut after servicing all stations?
Here's what I did, but I don't know if it's correct: (S.k denotes 'S of k')
S.k=(2t + 2(t+s)+...+2(t+(k-1)s))n
= n((k/2)(2(2t)+(k-1)2s))
= n((k(4t+2sk-2s))/(2))
= n((4kt+2sk^2-2sk)/(2))
= n(kt+sk^2+sk)
= nk(t+sk+s) yards
Q: There are k animal feeding stations arranged in a line with a supply hut. The stations are s yards apart and the nearest is t yards from the hut. An attendant carries n bags of feed, one at a time, to each feeding station. How far will he have traveled when he arrives back at the hut after servicing all stations?
Here's what I did, but I don't know if it's correct: (S.k denotes 'S of k')
S.k=(2t + 2(t+s)+...+2(t+(k-1)s))n
= n((k/2)(2(2t)+(k-1)2s))
= n((k(4t+2sk-2s))/(2))
= n((4kt+2sk^2-2sk)/(2))
= n(kt+sk^2+sk)
= nk(t+sk+s) yards