Answer :
Sure, let's work through the problem step-by-step.
We are given that a sea-exploring ship is pulling up a diver at the rate of 25 feet per minute. The diver was initially 200 feet below sea level. We need to find out how deep the diver was 10 minutes ago.
1. Understand the given information:
- Initial depth of the diver: 200 feet below sea level
- Ascent rate: 25 feet per minute
- Time elapsed: 10 minutes
2. Calculate the depth the diver ascended in 10 minutes:
- Ascent per minute: 25 feet
- Time elapsed: 10 minutes
The diver ascended:
[tex]\[
\text{Depth ascended} = \text{Ascent per minute} \times \text{Time elapsed}
\][/tex]
Substituting the given values:
[tex]\[
\text{Depth ascended} = 25 \, \text{feet/min} \times 10 \, \text{minutes} = 250 \, \text{feet}
\][/tex]
3. Calculate the new depth:
- Initial depth: 200 feet below sea level
- Depth ascended: 250 feet
Since the diver is ascending, we subtract the depth ascended from the initial depth:
[tex]\[
\text{New depth} = \text{Initial depth} - \text{Depth ascended}
\][/tex]
Substituting the values:
[tex]\[
\text{New depth} = 200 \, \text{feet} - 250 \, \text{feet} = -50 \, \text{feet}
\][/tex]
4. Interpret the new depth:
- A negative depth indicates that the diver is now 50 feet above sea level.
Therefore, 10 minutes ago, the diver was 250 feet deeper than the current position of 200 feet below sea level, which means the diver was initially below the sea at a depth of 200 feet. However, after ascending, the diver ended up 50 feet above the sea level.
In summary, the diver's depth 10 minutes ago was 250 feet deeper than the current depth, which places the diver 50 feet above sea level now.
We are given that a sea-exploring ship is pulling up a diver at the rate of 25 feet per minute. The diver was initially 200 feet below sea level. We need to find out how deep the diver was 10 minutes ago.
1. Understand the given information:
- Initial depth of the diver: 200 feet below sea level
- Ascent rate: 25 feet per minute
- Time elapsed: 10 minutes
2. Calculate the depth the diver ascended in 10 minutes:
- Ascent per minute: 25 feet
- Time elapsed: 10 minutes
The diver ascended:
[tex]\[
\text{Depth ascended} = \text{Ascent per minute} \times \text{Time elapsed}
\][/tex]
Substituting the given values:
[tex]\[
\text{Depth ascended} = 25 \, \text{feet/min} \times 10 \, \text{minutes} = 250 \, \text{feet}
\][/tex]
3. Calculate the new depth:
- Initial depth: 200 feet below sea level
- Depth ascended: 250 feet
Since the diver is ascending, we subtract the depth ascended from the initial depth:
[tex]\[
\text{New depth} = \text{Initial depth} - \text{Depth ascended}
\][/tex]
Substituting the values:
[tex]\[
\text{New depth} = 200 \, \text{feet} - 250 \, \text{feet} = -50 \, \text{feet}
\][/tex]
4. Interpret the new depth:
- A negative depth indicates that the diver is now 50 feet above sea level.
Therefore, 10 minutes ago, the diver was 250 feet deeper than the current position of 200 feet below sea level, which means the diver was initially below the sea at a depth of 200 feet. However, after ascending, the diver ended up 50 feet above the sea level.
In summary, the diver's depth 10 minutes ago was 250 feet deeper than the current depth, which places the diver 50 feet above sea level now.
