# 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?

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by sweetysiri92

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by sweetysiri92

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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**

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