Question

Between 10 P.M. and

7:45 A.M., the water level in a swimming pool
decreased by 13/16 inch.
Assuming that the water level decreased at a
constant rate, how much did it drop each hour?​

Answer 1

`(1)/(12)` inches per hour.

Explanation:

Between 10 P.M. and 7:45 A.M., the water level in a swimming pool decreased by
`(13)/(16)` inch.

First we calculate the hours between 10:00 P.M and 7:45 A.M.

10:00 P.M. = 22:00 P.M.

10:00 p.m. + 2 hours = 12:00 a.m.

so 2 hours + 7 hours and 45 minutes = 9 hours 45 minutes

9 hours 45 minutes =
`9(3)/(4)` =
`(39)/(4)` hours

It takes
`(39)/(4)` hours to decrease the water level by
`(13)/(16)` inches.

In 1 hour the water level would decrease =
`((13)/(16))/((39)/(4) )`

=
`(13)/(16)` ×
`(4)/(39)`

=
`(13)/(4* 39)`

=
`(13)/(156)`

=
`(1)/(12)` inches/hour

The water level decreased at a
`(1)/(12)` inches each hour.

Answer 2

The water level dropped
`(1)/(12)` inch each hour

Explanation:

- Between 10 P.M. and 7:45 A.M., the water level in a swimming pool

decreased by 13/16 inch

- Assuming that the water level decreased at a constant rate

- We need to find the drop each hour that means the unit rate of

decreased of the level of the water

- At first lets hind how many hours between 10 P.M. and 7:45 A.M.

∵ Between 10 P.M. and mid-night 2 hours

∵ Between mid-night and 7:45 A.M. 7 hours and 45 minutes

- Lets change 7 hours and 45 minutes to hours

∵ 1 hour = 60 minutes

∴ 45 minutes = 45 ÷ 60 =
`(3)/(4)` hours

∴ 7 hours and 45 minutes =
`7(3)/(4)` hours

∴ The total hours between 10 P.M. and 7:45 A.M. = 2 +
`7(3)/(4)` hours

∴ The total hours between 10 P.M. and 7:45 A.M. =
`9(3)/(4)`

∵ The unit rate of decreased = The decreased level ÷ total hours

∵ The decreased level is
`(13)/(16)` inche

∵ The total hours =
`9(3)/(4)` hours

- Lets change the mixed number
`9(3)/(4)` to improper fraction

∵
`9(3)/(4)` =
`((9*4)+3)/(4)`

∴
`9(3)/(4)` =
`(39)/(4)`

∵ The unit rate of decreased =
`(13)/(16)` ÷
`(39)/(4)`

- To solve the division of 2 fractions change the division sign to

multiplication sign and reciprocal the fraction after the division sign

∴ The unit rate of decreases =
`(13)/(16)` ×
`(4)/(39)`

∴ The unit rate of decreases =
`(1)/(12)` inch per hour

The water level dropped
`(1)/(12)` inch each hour