Question

Between 10 P.M. and

Answer 1

Answer:

The water level dropped $\frac{1}{12}$ inch each hour

Step-by-step 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 = $\frac{3}{4}$ hours

∴ 7 hours and 45 minutes = $7\frac{3}{4}$ hours

∴ The total hours between 10 P.M. and 7:45 A.M. = 2 + $7\frac{3}{4}$ hours

∴ The total hours between 10 P.M. and 7:45 A.M. = $9\frac{3}{4}$

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

∵ The decreased level is $\frac{13}{16}$ inche

∵ The total hours = $9\frac{3}{4}$ hours

- Lets change the mixed number $9\frac{3}{4}$ to improper fraction

∵ $9\frac{3}{4}$ = $\frac{(9*4)+3}{4}$

∴ $9\frac{3}{4}$ = $\frac{39}{4}$

∵ The unit rate of decreased =  $\frac{13}{16}$ ÷  $\frac{39}{4}$

- 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 =  $\frac{13}{16}$ × $\frac{4}{39}$

∴ The unit rate of decreases = $\frac{1}{12}$ inch per hour

The water level dropped $\frac{1}{12}$ inch each hour

Answer 2

Answer:

$\frac{1}{12}$ inches per hour.

Step-by-step explanation:

Between 10 P.M. and 7:45 A.M., the water level in a swimming pool decreased by  $\frac{13}{16}$ 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 =  $9\frac{3}{4}$ =  $\frac{39}{4}$ hours

It takes  $\frac{39}{4}$ hours to decrease the water level by  $\frac{13}{16}$ inches.

In 1 hour the water level would decrease = $\frac{\frac{13}{16}}{\frac{39}{4} }$

=  $\frac{13}{16}$ ×  $\frac{4}{39}$

=  $\frac{13}{4\times 39}$                                                        

=  $\frac{13}{156}$

=  $\frac{1}{12}$ inches/hour

The water level decreased at a $\frac{1}{12}$ inches each hour.