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

Answer and explanation:

Let depth of equipment elevator = de

Let depth of miners elevator =dm

Since equipment elevator de descends at the velocity of 4feet per second

equipment depth de =4s

Since miners elevator dm descends at velocity of 15feet per second dm=15s

however miner elevator would delay by 30 seconds before descending so it is given by 15(s-30)

in order to find out depth of each elevator, we calculate time spent descending for each elevator, equipment elevator descended 30 seconds before miner started descending for 14 seconds so total time is 44 seconds. We plug 44 into their equations

so that

De=4s=4*44=176feet

Dm=15(s-30)=15*44-30=210feet

Therefore even though equipment elevator began descending 30 seconds before miner elevator, it would still be 210-176=34feet deeper in depth when descending after 14seconds compared to equipment elevator

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