The water level in a pool is currently at 1/2 of an inch. Every hour, the water level increases 4.75 inches. How many hours will it take the water level to reach 33.75 inches?

7.1 hours

Step-by-step explanation:

Given data

Let the number of hours taken to fill the pool be x

the current quantity is 1/2 the capacity of the pool

we are given that the rate of flow = 4.75 in per hour

let the total amount of water after x hours be y, the expression for the quantity of water is given as

if y= 33.75 in, let us find x

divide both sides by 4.75

Hence, it will take 7.1 hours

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584