Depth- Maximum

[Guest]

A diver is working 20 ft. below the surface of the water. The distance between the water and the deck of his ship is 1/8 of available air hose, and 2/3 of the total length remains on the storage reel. Determine maximum working depth of the diver without changing equipment.

Let H = hose

My partial solution:

1/8 + 2/3H + 20

How do I continue ? Thank you.

[Guest]

H/8 + 2H/3 + 20 = H
Find H
Then depth = 20 - H/8

[Guest]

Sorry should be.....
H/8 + 2H/3 + 20 = H
Find H
Then depth = H - H/8 = 7H/8

[Guest]

H/8 + 2H/3 + 20 = H

3H + 16H + 480 = H

19H + 480 = H

18H = 480

18H/18 = 480/18

H = 26.6666= 27 ft.

27 - 27/3 = 7(27)/8

27 - 9 = 189/8

18 = 23.625 = 24

??

[Guest]

H/8 + 2H/3 + 20 = H
Find H
Then depth = H - H/8 = 7H/8

H/8 + 2H/3 + 20 = H
multiply across by 24....

3H + 16H + 480 = 24H

480 = 24H - 19H

480 = 5H

96 = H = Total hose
96/8 = 12 = dist from water to deck
Depth = 96 - 12 = 84 feet OR 7H/8 = 84 feet

[Guest]

Thanks.

One question:

What does the 7H/8 represent ?

[Guest]

H/8 is H divided by 8 or one eighth of eight.
7H/8 is seven times H/8.....or...seven eights of H.
H itself is all of H ...so it is 8 eights of H.

Therefore H - H/8 is eight eighths minus one eighth gives seven eighths

[Guest]

Thanks again - I understand now.