The first thing you should do is graph the following lines
2x + 3y = 8
x-2y = -3
x = 0
y = 0
After you have graphed them, you should proceed to evaluate points in the xy plane that meet the following restrictions:
2x + 3y≤8, x-2y≥-3, x≥0, y≥0
The resulting region is the region "R" shown in the attached graph.
Tangent = opposite/adjacent
tangent = 15 / 8
If opp = 15 and adj = 8 then
hypotenuse^2 = 15^2 + 8^2
hypotenuse^2 = 225 + 64
hypotenuse^2 = 289
hypotenuse = 17
secant = hypotenuse / adjacent
secant = 17 / 8
secant = 2.125
The sides could be 1,14 or 2,7
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.
Good afternoon.
120square --- 34h
x square --- 1h
34x = 120
x = 120/34
x = 3,5 square
