A scientist uses a submarine to study ocean life.
She begins at sea level, which is an elevation of 0 feet.
She travels down 21.1 feet.
She then ascends 19.1 feet.
Next, she travels down a second time, 80.7 feet.
How many feet must she now ascend to get back to sca
level?
The correct answer and explanation is:
To determine how many feet the scientist must ascend to return to sea level, we can break the problem into stages and track her movement step by step:
- Starting at Sea Level: The scientist begins at sea level, which is at 0 feet.
- First Descent: She descends 21.1 feet. This means she is now 21.1 feet below sea level. We can express this as: 0−21.1=−21.1 feet0 – 21.1 = -21.1 \text{ feet} So, her position after the first descent is at -21.1 feet.
- First Ascent: She ascends 19.1 feet. Ascending means moving toward sea level, so we add 19.1 feet to her current position of -21.1 feet: −21.1+19.1=−2.0 feet-21.1 + 19.1 = -2.0 \text{ feet} After the first ascent, she is now 2 feet below sea level.
- Second Descent: She descends again, this time by 80.7 feet. To find her new position, we subtract 80.7 feet from -2.0 feet: −2.0−80.7=−82.7 feet-2.0 – 80.7 = -82.7 \text{ feet} After the second descent, she is now 82.7 feet below sea level.
- Final Ascent: To return to sea level, she must ascend from -82.7 feet back to 0 feet. The total distance she needs to ascend is the absolute value of her current depth, which is: 82.7 feet82.7 \text{ feet}
Therefore, the scientist must ascend 82.7 feet to return to sea level.
This problem involves basic arithmetic operations—addition and subtraction—where the key is to track the scientist’s position relative to sea level after each movement. By starting from 0 feet and moving up or down in increments, we can calculate how much she must ascend to return to the starting point.