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Question 885553: the ratio of land to water is 1:2 for the whole world, the above ratio is 2:3 for northern hemisphere. what is the above ratio on the southern hemisphere?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the total square feet of land in the world.
since the ratio of land to water is 1/2, this mean that the total square feet of water in the world is 2x
the total combined land and water in the world is therefore 3x.
the northern hemisphere is one half of this and the southern hemisphere is one half of this, so we get.
total of land and water in the northern hemisphere is 1.5x.
total of land and water in the southern hemisphere is 1.5x.
in the northern hemisphere, the ratio of land to water is 2/3.
this means that 2/5 of the northern hemisphere is covered by land and 3/5 of the northern hemisphere is covered by water.
2/5 * 1.5x = .6x
3/5 * 1.5x = .9x
since the total land in the world is equal to x, this means that the southern hemisphere must have x - .6x = .4x of land.
since the total water in the world is equal to 2x, this also means that the southern hemisphere must have 2x - .9x = 1.1x of water.
the ratio of land to water in the southern hemisphere is therefore .4 to 1.1 which is the same as 4/11.
let's see if this makes sense.
the total of land and water in both north and south hemispheres is equal to 3x which allows for 1.5x in the north and 1.5x in the south.
this can also be written as 3/2*x in the north and 3/2*x in the south.
the ratio of land to water in the north is 2/3 which means 2/5 of the total area is land and 3/5 of the total area is water.
since the total area is 3/2 * x, this means that:
2/5 * 3/2 * x = 6/10 * x is land
3/5 * 3/2 * x = 9/10 * x is water.
the ratio of land to water in the south is 4/11 which means that 4/15 of the total area is land and 11/15 of the total area is water.
since the total area is 3/2 * x, this means that:
4/15 * 3/2 * x = 12/30 * x is land.
11/15 * 3/2 * x = 33/30 * x is water.
the total land area in the world is equal to 6/10 * x in the north and 12/30 * x in the south which gets you a total of 18/30 * x + 12/30 * x which is equal to 30/30 * x which is equal to x area of land in the world.
the total water area in the world is equal to 9/10 * x in the north and 33/30 * x in the south which gets you a total of 27/30 * x in the north and 33/30 * x in the south which is equal to 60/30 * x which is equal to 2 * x area of water in the world.
the overall ratio of land to water is therefore equal to x / 2 * x which is equal to 1/2 which is here we started so the ratios are good.
the ratios are:
1 to 2 land to water ratio overall
2 to 3 land to water ratio northern hemisphere.
4 to 11 land to water ratio southern hemisphere.
if x's bother you, you can also confirm this with numbers.
assume the total area in the world is equal to 6 million acres.
this is not a real number, but should be good enough to figure out what we need to do.
divide this into north and south and the north gets 3 million acres and the south gets 3 million acres.
the ratio of land to water in the north is 2 to 3 which means that 2/5 of the area is land and 3/5 of the area is water.
this gives the north 1.2 million acres of land and 1.8 acres of water.
the ratio of land to water in the south is 4/11 which means that 4/15 of the area is land and 11/15 of the area is water.
this gives the south .8 million acres of land and 2.2 million acres of water.
add up all the area of land in the world and water in the world and you get:
total land = north land and south land = 1.2 + .8 = 2 million acres.
total water = north water and south water = 1.8 + 2.2 = 4 million acres.
total acres in the world is 6, 2 of which are land and 4 of which are water.
overall ratio of land to water in the world holds so the numbers are good.
the solution to this problem is the ratio of land to water in the southern hemisphere is 4 to 11.
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