Question 1145904: This is a question from my son's test. He got (a) correct but (b)wrong. He doesn't understand why. Would appreciate an explanation that can help him understand his mistake.
A submarine is at −750 feet or 750 feet below sea level. It descended 300 feet, then ascended 550 feet, and then descended 425 feet.
a. Write and evaluate a numerical expression to find the submarine’s final elevation. His answer is -925 feet which is correct.
b. The submarine next descended to the ocean floor, which was at an elevation of −2,250 feet. How far did the submarine descend?
He answered -1325 feet because according to his understanding the submarine descended so should be negative. However, the correct answer should be 1325 ft (not - 1325 ft). Please help him understand why.
Greatly appreciate your help, as always.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! He answered -1325 feet because according to his understanding the submarine descended so should be negative. However, the correct answer should be 1325 ft (not - 1325 ft). Please help him understand why.
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It's semantics.
It descended 1325.
Descent assumes negative.
It ascended -1325 feet.
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consider a "round trip."
If it starts at the surface, descends 1000 feet, then ascends 1000 feet, it's back at the surface.
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Descent of +1000 ft = -1000 feet
Ascent = +1000 feet
The sum is zero.
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Answer by ikleyn(52790)  (Show Source):
You can put this solution on YOUR website! .
(a) This sentence and this sequence of maneuvering mathematically is translated into this formula for the elevation
elevation = -750 - 300 + 550 - 425 = my calculation = -925,
exactly as your son got it.
Initial elevation of -750 ft below the sea level is given.
Descending 300 ft means subtracting 300 ft from the current elevation to get new elevation.
Ascending 550 ft means adding 550 ft to the current elevation to get new elevation.
So far everything is very natural.
(b) The submarine descended from the level of -925 ft to the ocean floor at the elevation -2250 ft.
How far it descended ?
Intuitively, it is clear: it descended 2250 - 925 = 1325 ft (use your common sense).
If you (or your son, or the teacher) wants use mathematic expression (equation) at this point,
he can write -925 - descending = -2250, which gives
-925 + 2250 = descending, or
descending = -925 + 2250 = 1325 ft (the correct answer).
Memorize it: descending X ft means new_level = old_level - X feet;
ascending X ft means new_level = old_level + X feet.
Hope it helps.
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