SOLUTION: In an expression, define variable for time rode in the elevator and use variable to write rule for depth below the surface.
The deep mine is 12,720 feet deep. An elevator takes
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Question 626996: In an expression, define variable for time rode in the elevator and use variable to write rule for depth below the surface.
The deep mine is 12,720 feet deep. An elevator takes miners up at the rate of 20 feet per second. Assume that the number of feet below the surface is a negative number.
1. If the miners get on this elevator at the bottom of the shaft and ride it for 40 seconds, how far are they still below the surface?
2. In how many seconds will the miners be 6,000 feet below the surface?
3. f they ride the elevator for three and three-quarter minutes, how far below the surface are they?
4. How long does it take the miners to reach the surface?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Your problem doesn't specify the speed when the elevator is going down, and there is no reason to assume that the speed going up and the speed going down is the same, hence the following function is only valid for modeling the situation where the elevator is going up.
Presuming that a miner could enter or exit the elevator at intermediate points between the bottom of the shaft and the surface, a start depth, 
must be specified.
The distance traveled in 
seconds is 
feet since the elevator rises at 20 feet per second.
Taking into account that is a distance below ground and is therefore a negative number, we write:
\ =\ 20t\ +\ h_o)
where
and
\ =\ \left\{t\ \in\ \mathbb{R}\ |\ 0\ \leq\ t\ \leq\ \frac{h_o}{20}\right\})
and
\ =\ \left\{h(t)\ \in\ \mathbb{R}\ |\ h_o\ \leq\ h(t)\ \leq\ 0\right\})
John
My calculator said it, I believe it, that settles it
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