help:

Two travelers start simultaneously in two cities A and B, and go to meet each other. The part of A walk 1 km on the first day , the second day 2 km , 3 km on the third day , and so on. The part of B walk 20 miles the first day, the second day 18 km , 16 km on the third day and so on. If the distance between A and B is 165 km , then the two travelers were within :
a. 33 days .
b . 10 days .
c . 43 days .
d. 15 days .
e. 66 days

1 answer

Between them, A and B cover
22-n miles on the nth day.

You can see that this is an A.P. with
a = 22
d = -1

So, we want to find Sn such that Sn = 165. So,

n/2 (2*22+(n-1)(-1)) = 165
n = 9.2

So, on the 10th day they meet.
n =