Answer:
[tex]121\frac{7}{24}\text{ yards}[/tex] below sea level.
Step-by-step explanation:
We have been given that a submarine hovers at 66 and 2/3 yards below sea level. This means that the position of submarine is negative.
We can represent this information as:
[tex]-66\frac{2}{3}\text{ yards}[/tex]
We have been also given that the submarine ascends 24 and 1/8 yards. This means we need to add [tex]24\frac{1}{8}\text{ yards}[/tex] to [tex]-66\frac{2}{3}\text{ yards}[/tex].
[tex]-66\frac{2}{3}\text{ yards}+24\frac{1}{8}\text{ yards}[/tex]
[tex]-\frac{200}{3}\text{ yards}+\frac{193}{8}\text{ yards}[/tex]
[tex]-\frac{200*8}{3*8}\text{ yards}+\frac{193*3}{8*3}\text{ yards}[/tex]
[tex]-\frac{1600}{24}\text{ yards}+\frac{579}{24}\text{ yards}[/tex]
[tex]-\frac{1021}{24}\text{ yards}[/tex]
The submarine descends again 78 and 3/4 yards. This means we need to subtract [tex]-78\frac{3}{4}\text{ yards}[/tex] from [tex]-\frac{1021}{24}\text{ yards}[/tex].
[tex]-\frac{1021}{24}\text{ yards}-78\frac{3}{4}[/tex]
[tex]-\frac{1021}{24}\text{ yards}-\frac{315}{4}[/tex]
[tex]-\frac{1021}{24}\text{ yards}-\frac{315*6}{4*6}[/tex]
[tex]-\frac{1021}{24}\text{ yards}-\frac{1890}{24}[/tex]
[tex]-\frac{2911}{24}\text{ yards}[/tex]
[tex]-121\frac{7}{24}\text{ yards}[/tex]
Therefore, the submarine's new position is [tex]121\frac{7}{24}\text{ yards}[/tex] below sea level.
