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.

  • 3
    $\begingroup$ Descending $100$ feet means going downwards by $100$ feet. Descending $-100$ feet means going upward by $100$ feet. $\endgroup$ – Lubin Sep 28 '19 at 0:39
  • $\begingroup$ Thank you! This helps. $\endgroup$ – Pearl Sep 28 '19 at 18:53

This is rather simple really. If a submarine is going downwards, it's travelling a distance, regardless of direction. The question says 'How far did it descend?'. This is merely a distance and therefore requires a length. i.e a positive number. Because you can't have a negative length. If they asked 'Where is the submarine?' then your son's answer would be right. Same way you say a positive number for 'feet below see level'. If this is for an exam I recommend that he make sure he realizes if it is decelerate or accelerate or stuff like that. But from what I've gathered is that some exam boards aren't too fussed (But it's better to be safe than sorry)

  • $\begingroup$ Thank you, Yolo. I was looking for an explanation that would be logical and simple for him to understand based on what he has learned so far, not more advanced concepts, so this greatly helps. What would be the correct numerical expression to evaluate this? $\endgroup$ – Pearl Sep 28 '19 at 18:44
  • $\begingroup$ There really wouldn't be one. It's just spotting the wording of the question. So focus on three things: do you have a unit of measurement, what are you relating this to (as in is this distance relative to say a rock or a tree) and whether or not it is already implied a decrease or increase (Such as acceleration or deceleration) $\endgroup$ – yolo Sep 28 '19 at 18:50

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