21. higher order thinking a gold mine has two elevators, one for equipment and one for miners. one day, the…
21. higher order thinking a gold mine has two elevators, one for equipment and one for miners. one day, the equipment elevator begins to descend. after 28 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, how much deeper is the elevator for the miners?
Answer
Explanation:
Step1: Calculate the depth of the equipment elevator
The equipment elevator descends at a rate of 4 feet per second. It has been descending for $28 + 14=42$ seconds. Using the formula $d = r\times t$ (where $d$ is distance, $r$ is rate and $t$ is time), we have $d_{1}=4\times42 = 168$ feet.
Step2: Calculate the depth of the miners' elevator
The miners' elevator descends at a rate of 15 feet per second and has been descending for 14 seconds. Using the formula $d = r\times t$, we have $d_{2}=15\times14 = 210$ feet.
Step3: Calculate the difference in depth
To find out how much deeper the miners' elevator is, we subtract the depth of the equipment elevator from the depth of the miners' elevator. So, $\Delta d=d_{2}-d_{1}=210 - 168=42$ feet.
Answer:
The position of the equipment - elevator relative to the surface is 168 feet below the surface. The position of the miners' elevator relative to the surface is 210 feet below the surface. The miners' elevator is 42 feet deeper than the equipment elevator.