Hard math problem on global warming?

Question

When ice melts it takes up 92% of its original volume as ice. Let the total mass of earth's icecaps be x, and let y percent of this ice be above water. Express y in terms of x so that no change will occur if the ice caps melt completely.

Answer 1

You shouldn't be talking about mass but about volume. Whatever happens to the ice--if it melts, if it boils, there is NO change in mass. Only volume.

Let the total volume of earth's ice-caps be x; let y percent of this ice be above water.

For there to be no change in the sea level if all the ice melts completely, the ice above water must make up for the loss in volume of ice underwater--which becomes a smaller volume of water than it was as ice.

ice above water = x [times] (y/100) = (xy)/100

ice below water = x - (xy/100) = (100x-xy) / 100

when melted; ice that was above water has the volume
= 0.92 (xy/100)

when melted; ice that was below water = 0.92 ( 100x-xy)/100

how much less space does melted ice underwater take up than frozen ice
= 0.08 (100x-xy)/100

thus 0.08(100x-xy)/100 = 0.92 (xy/100)
8x-0.08xy = 0.92 xy
8x = xy
y = 8

...that's what I got. Do you have the answer?

Answer 2

That isn't right, if the water that's melted only takes up 92% of the volume that it held originally as ice then wouldn't the sea level drop if the icecaps melted? The reason ice floats is because it is less dense than water. Because the ice is less dense it is not displacing as much volume as it would if it melted. This is why the sea level will rise, the melted water will displace more volume than the ice currently is. Whoever wrote that question is wrong. (P.S I don't know the answer to your question).

Answer 3

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Answer 4

The ice is not floating, it rests on the ocean bottom. (Otherwise y would be a constant function of ice density). Mass below water / mass above water = ice volume below water v1 / ice volume above water v2 =
(1-y)/y. The ocean volume change from the ice below water dv1 =
-.08*v1 and from the ice above water dv2 = .92*v2. We want -dv1=dv2. Thus v1/v2=.92/.08= (1-y)/y. So y=.08, or 8%.
Note: You can't express y "in terms of x". It's a dimensionless number.

Answer 5

lol