Ever hear about the mathematician who drowned in the river that was on average 2-inches deep? The joke is slightly bemusing, however, it did start me pondering how the river could be set up so it could drown a man. I mean we most likely have heard that a baby can drown in two-inches of water, but a man is fairly improbable.
Here was the set up I came up with: You have a river that has the same characteristics up and down its length. So a cross-section will mimic the entire river system. It is 1,000 feet wide. The 1st section is 445 feet wide and is 1-inch deep. The middle section is 10 feet wide and is 100 inches deep, (8 1/3 feet.) The last section from the middle to the far bank is 445 feet wide and is 1-inch deep. To find the average depth of the river we add the 3 sections together after we have multiplied them by their depth. Then we divide it by the total width of the river. So
(445*1)+(10*100)+(445*1)=445+1000+445=1990
1990/1000=1.99 inches
So on average the river is 1.99 inches deep, but you can see how this can be tricky for the man fording it.
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