A gold mine has two​ elevators, one for equipment and another for the miners. The equipment elevator descends 6 feet per second. The elevator for the miners descends 17 feet per second. One​ day, the equipment elevator begins to descend. After 22 ​seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 14 ​seconds? At that​ time, which elevator is​ deeper?

Question

Question content area bottom
Part 1
The position of the equipment elevator relative to the surface is
  
enter your response here feet.

Answer 1

To find the position of the equipment elevator after 22 seconds and then another 14 seconds (total of 36 seconds), follow these steps:

1. Calculate the position of the equipment elevator after 36 seconds:

   • It descends at a rate of 6 feet per second.
   • After 36 seconds: \[ \text{Position} = \text{Rate} \times \text{Time} = 6 , \text{feet/second} \times 36 , \text{seconds} = 216 , \text{feet} \]

2. Calculate the position of the miners' elevator:

   • The miners' elevator starts descending after 22 seconds, so it descends for 14 seconds.
   • The rate for this elevator is 17 feet per second.
   • After 14 seconds: \[ \text{Position} = \text{Rate} \times \text{Time} = 17 , \text{feet/second} \times 14 , \text{seconds} = 238 , \text{feet} \]

3. Compare the positions:

   • The equipment elevator is at \(216\) feet.
   • The miners' elevator is at \(238\) feet.

From this information, you can conclude:

• The position of the equipment elevator relative to the surface is 216 feet.

Now, regarding which elevator is deeper:

• Since 238 feet (miners' elevator) is greater than 216 feet (equipment elevator), the miners' elevator is deeper.