Question

Between 10 P.M and 7:20 A.M., the water level in a swimming pool decreased by 7/12 in. Assuming that the water level decreased at a constant rate, how much did the water level drop each hour? PLEASE HELP I DONT GET THIS AT ALL!​

Answer 1

0.0625 or
`(1)/(16)`

Explanation:

Interpreting the Problem

If the water level decreases at a constant rate, then that just means that the relationship between the water level and time is linear or is a straight line if graphed.

Calculating Constant Rate:

let's just say that:
`C = \text{ contant rate the water level dropped at each hour}`

this means if we added C by how many hours passed, we should get the amount the water level dropped:
`C+C+C+C\text{...how many hours passed} =(7)/(12)`

let's also just say that:
`H = \text{ amount of hours that passed}`

from here we can rewrite the equation using multiplication:
`CH = (7)/(12)`

we can now divide both sides to isolate C:
`C = ((7)/(12))/(H)`, so now all we have to do is find how many hours passed.

From 10 P.M to 12 A.M, 2 hours pass. From 12 A.M to 7 A.M, 7 hours pass and from 7 A.M to 7:20 A.M, 20 minutes pass

So we have:
`2 \text{ hours} + 7 \text{ hours} + 20 \text{ minutes} = 9\text{ hours} + 20\text{ minutes}`

We want to represent this as one value and also in hours, so we'll need to convert the minutes to hours. To see how many 20 minutes is to one hour, we simply divide this 20 minutes by how many minutes are in an hour, which is 60 minutes:
`(20)/(60) = (1)/(3)`

It's actually super useful to keep this in fraction form, and even convert the 9 hours to fraction form:
`9 + (1)/(3) = (27)/(3) + (1)/(3) = (28)/(3)`

Now from here, we know that:
`H = (28)/(3)`

so let's plug this into the expression we made!
`C = ((7)/(12))/((28)/(3))\implies (7)/(12) * (3)/(28)`

before multiplying, we can rewrite 12 as (4 * 3) so we can cancel out the 3 in the numerator and denominator making the simplification process a bit easier. We can also rewrite 28 as (4 * 7) to cancel out the 7 in the numerator and denominator:
`C = (7 * 3)/((4 * 3) * (7 * 4)) = (1)/(16) = 0.0625`

This means if we multiplied the 1/16 or 0.0625 by the 9.33333 hours that passed we would get the total amount that decreased: 7/12