How deep is each lake?

Question

The surface of Big Lake is 31 ft above the surface of Long Lake. Long Lake is half as deep as Big Lake and the bottom of Long Lake is 8 ft below the bottom of Big Lake. Clear Lake's surface is 10 ft below the surface of Big Lake and its bottom is 6 ft above the bottom of Long Lake. How deep is each lake?


Please help.. thank you =)

I sketched them to try and figure out the answer.
I think Long Lake is 23 ft deep, Big Lake is 46 ft, and Clear Lake is 46 ft. Is this right?

..and is this statement correct about the lakes...?
Clear Lake is 2 ft below Big Lake.

again..Thank you so much ^_^

Answer 1

Let L be the depth of Long Lake. If we use the bottom of Long Lake as our zero point, then the bottom of Big Lake is at 8, the top of Long Lake is at L, and the top of Big Lake is at 8 + 2L, and 8 + 2L = L + 31. Solving for L gives L = 23, and the depth of Big Lake is 2L = 46, and the top of Big Lake is at 54. The top of Clear Lake is at 54 - 10 = 44, and the bottom of Clear Lake is at 6, and so the depth of Clear Lake is 44 - 6 = 38.
The bottom of Clear Lake is 2 feet below the bottom of Big Lake , just as you say, but the top of Clear Lake is 10 feet below the top of Big Lake.

Answer 2

let x = long lake depth; 2x = big lake depth; y = clear lake

31 + (x - 8) = 2x

from this you will get that x = 23; so 2x = 46... you pretty much got that right :)

then next is clear lake which surface is 10 ft below big lake's (or 21 ft above long lake) and bottom is 6 ft above long lake's, thus:

21 + (x - 6) = y

recheck the answer you got before u submitted your quetion if it's the same as the one you'll get from the above formula (replacing x with long lake's depth)

and you're right, clear lake's bottom if 2ft below big lake's

Answer 3

sorry suck at math...