Question

A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 5 feet per second. The elevator for the miners descends 13 feet per second. One day, the equipment elevator begins to descend. After 23 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?

A) Equipment elevator: 85 feet, Miners elevator: 231 feet. Miners elevator is deeper.
B) Equipment elevator: 115 feet, Miners elevator: 241 feet. Equipment elevator is deeper.
C) Equipment elevator: 95 feet, Miners elevator: 251 feet. Miners elevator is deeper.
D) Equipment elevator: 125 feet, Miners elevator: 261 feet. Equipment elevator is deeper.

Answer 1

The correct option is B) Equipment elevator: 115 feet, Miners elevator: 241 feet. Because equipment elevator is deeper.

Step-by-step explanation:

The key to solving this problem is to calculate the distance each elevator travels during the specified time intervals.

The equipment elevator descends for 23 seconds before the miners' elevator starts moving.

In these 23 seconds, the equipment elevator covers a distance of
`\(23 \, \text{seconds} * 5 \, \text{feet/second} = 115 \, \text{feet}\).`

Now, the miners' elevator begins descending 18 seconds after the equipment elevator, covering a distance of
`\(18 \, \text{seconds} * 13 \, \text{feet/second} = 234 \, \text{feet}\)` during this time.

To find the final positions, add the distances covered by each elevator to their initial positions.

The equipment elevator is initially at the surface, so its final position is
`\(0 + 115 = 115 \, \text{feet}\).`The miners' elevator's initial position is also at the surface, so its final position is
`\(0 + 234 = 234 \, \text{feet}\).`

Comparing the final positions, the equipment elevator is at 115 feet, and the miners' elevator is at 234 feet.

Therefore, the equipment elevator is deeper.

The correct answer is option B) Equipment elevator: 115 feet, Miners elevator: 241 feet. Because equipment elevator is deeper.