Question

A submarine hovers at 66 and 2/3 yards below sea level. If it ascends 24 and 1/8 yards and then descends again 78 and 3/4 yards, what is the submarine’s new position, in yards, below sea level?

Answer 1

121 7/24

Explanation:

Answer 2

`121(7)/(24)\text{ yards}` below sea level.

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:

`-66(2)/(3)\text{ yards}`

We have been also given that the submarine ascends 24 and 1/8 yards. This means we need to add
`24(1)/(8)\text{ yards}` to
`-66(2)/(3)\text{ yards}`.

`-66(2)/(3)\text{ yards}+24(1)/(8)\text{ yards}`

`-(200)/(3)\text{ yards}+(193)/(8)\text{ yards}`

`-(200*8)/(3*8)\text{ yards}+(193*3)/(8*3)\text{ yards}`

`-(1600)/(24)\text{ yards}+(579)/(24)\text{ yards}`

`-(1021)/(24)\text{ yards}`

The submarine descends again 78 and 3/4 yards. This means we need to subtract
`-78(3)/(4)\text{ yards}` from
`-(1021)/(24)\text{ yards}`.

`-(1021)/(24)\text{ yards}-78(3)/(4)`

`-(1021)/(24)\text{ yards}-(315)/(4)`

`-(1021)/(24)\text{ yards}-(315*6)/(4*6)`

`-(1021)/(24)\text{ yards}-(1890)/(24)`

`-(2911)/(24)\text{ yards}`

`-121(7)/(24)\text{ yards}`

Therefore, the submarine's new position is
`121(7)/(24)\text{ yards}` below sea level.