To find the final depth of the scuba diver after both descents, we can first convert the mixed numbers to improper fractions, sum them, and then analyze the result in relation to sea level.
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Convert the mixed numbers to improper fractions:
- For \( 19 \frac{5}{12} \): \[ 19 \frac{5}{12} = \frac{19 \times 12 + 5}{12} = \frac{228 + 5}{12} = \frac{233}{12} \]
- For \( 3 \frac{3}{5} \): \[ 3 \frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5} \]
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Find a common denominator to add the fractions:
- The least common multiple of 12 and 5 is 60.
- Convert \( \frac{233}{12} \) to a fraction with a denominator of 60: \[ \frac{233}{12} = \frac{233 \times 5}{12 \times 5} = \frac{1165}{60} \]
- Convert \( \frac{18}{5} \) to a fraction with a denominator of 60: \[ \frac{18}{5} = \frac{18 \times 12}{5 \times 12} = \frac{216}{60} \]
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Add the two fractions: \[ \frac{1165}{60} + \frac{216}{60} = \frac{1165 + 216}{60} = \frac{1381}{60} \]
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Convert the improper fraction back to a mixed number:
- Divide 1381 by 60:
- 60 goes into 1381 twenty-three times (since \( 60 \times 23 = 1380 \)).
- Remainder: \( 1381 - 1380 = 1 \).
- Thus, \[ \frac{1381}{60} = 23 \frac{1}{60} \]
- Since both descents were below sea level, the location of the scuba diver in relation to sea level is \(-23 \frac{1}{60}\) feet.
- Divide 1381 by 60:
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Conclusion: After both descents, the scuba diver is \(-23 \frac{1}{60}\) feet below sea level.
Thus, the correct answer is:
B. The location of the scuba diver in relation to sea level was -23 1/60 feet.
3 answers