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 13 feet per second. One​ day, the equipment elevator begins to descend. After 33 ​seconds, the elevator for the miners begins to descend. What is the position of each elevator relative to the surface after another 12 ​seconds? At that​ time, which elevator is​ deeper?

Answer 1

The position of the equipment elevator is 180 feet deep

The position of the miner's elevator is 156 feet deep

The equipment elevator is deeper.

Explanation:

From the question,

For the equipment elevator

Velocity (v) = 4 feet/second

and for the miner's elevator,

Velocity (v) = 13 feet/second

To determine the position of each elevator, the position can be related to the distance covered.

From

Velocity = Distance / Time

Distance = Velocity × Time

Now, from the question,

The equipment elevator first descends for 33 seconds, after which the miner's elevator then start to descend both elevators descend for another 12 seconds. That is, the equipment elevator descends for a total of (33+12) seconds while the miner's elevator descends for 12 seconds.

Now, for the equipment elevator

Velocity = 4 feet/second

Time = (33 + 12 seconds) = 45 seconds

From

Distance = Velocity × Time

Distance = 4 × 45

Distance = 180 feet

The position of the equipment elevator is 180 feet deep

For the miner's elevator,

Velocity = 13 feet/second

Time = 12 seconds

Also, from

Distance = Velocity × Time

Distance = 13 × 12

Distance = 156 feet

The position of the miner's elevator is 156 feet deep

Hence, the equipment elevator is deeper.