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Let represent the depth of the miner and equipments elevator, respectively. We know that equipment elevator descends with a velocity of
feet per second, and the miners one descends with a velocity of
feet per second.
If we start counting time () when the equipment elevator begins to descend, after
seconds its depth will be
On the other hand, the miner elevator follows the same rule, but we have to use its velocity, and remember that it starts with a delay of thirty seconds:
Now, we have to wait the 30 seconds of delay, and then another 14 seconds. This means that we want to know the positions of both elevators when . Let's plug this value into the two equations:
So, the equipment elevator is 176 feet deep, and the miner elevator is 210 feet deep, and thus this is the deeper one.
The absolute value returns the "positive version" of a number.
In other words, if the number is positive, it remains positive; if the number is negative, it changes sign.
So, if we want , we want the "positive version" of x to be 9.
This can happen in two ways: if x is already 9, then its absolute value is still nine. If instead x=-9, its positive value will be 9 again.
In formula, we have
because