Question

 A gold mine has two​ elevators, one for equipment and another for the miners. The equipment elevator descends 4 feet per second. The elevator for the miners descends 14 feet per second. One​ day, the equipment elevator begins to descend. After 21 ​seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 18 ​seconds? At that​ time, which elevator is​ deeper?

Answer 1

To solve the problem, we will calculate the position of both elevators relative to the surface after the given time intervals.

### Equipment Elevator:
- **Descends at**: 4 feet per second
- **Time of descent before miners' elevator starts**: 21 seconds
- **Additional descent time**: 18 seconds

1. **Total descent time for equipment elevator**:
\[
21 + 18 = 39 \text{ seconds}
\]

2. **Depth of equipment elevator**:
\[
\text{Depth} = \text{Rate} \times \text{Time} = 4 \, \text{ft/s} \times 39 \, \text{s} = 156 \text{ feet}
\]

### Miners Elevator:
- **Descends at**: 14 feet per second
- **Starts descending after**: 21 seconds
- **Total descent time for miners' elevator**: 18 seconds

1. **Time of descent for miners' elevator**:
\[
18 \text{ seconds}
\]

2. **Depth of miners elevator**:
\[
\text{Depth} = \text{Rate} \times \text{Time} = 14 \, \text{ft/s} \times 18 \, \text{s} = 252 \text{ feet}
\]

### Summary:
- **Position of equipment elevator after 39 seconds**: 156 feet below the surface
- **Position of miners elevator after 18 seconds (starting at 21 seconds)**: 252 feet below the surface

### Conclusion:
The miners' elevator is deeper than the equipment elevator after the specified times. The miners' elevator is at 252 feet below the surface, while the equipment elevator is at 156 feet below the surface.