Question

During one year a beach eroded 1.2 m to a line 48.3 m from the wall of a building. if the erosion is 0.1 m more each year than the previous year, when will be the waterline reach the wall?

Answer 1

in 21 years

Let us during the previous year beach erosion was : 1.2 m.
Every year it increases by 0.1m. So this year 1.3m next year 1.4m and so on. This is clear ly arithmatic progression.

Sum of erosion amounts up to n years from now should be >= 48.3 meters for the waterline to touch the wall.

so  Sn = 1.3 + 1.4 + 1.5 + .... n terms >= 48.3
           = [ 2*1.3 + (n-1)0.1 ] * n/2 >= 48.3

2.5 n + 0.1 n² - 96.6 >= 0
n² + 25 n - 966 >= 0

Δ = 4489        n = (- 25 +- 67) /2  =  21 years

SO n >= 21 years