A building has two elevators that both go above and below ground. At a certain time of day the travel time it takes elevator A to reach height h in meters is 0.8h+16. The travel time it takes elevator B to reach height h in meters is - 0.8h+12 seconds. what is the height of each elevator at this time? If they travel towards one another, at what height do they pass each other? and how long would it take? If you are on an underground parking level 14 meters below ground which elevator would reach first?

Step-by-step explanation:

We have been given that a building has two elevators that both go above and below ground.

At a certain time of day the travel time it takes elevator A to reach height h in meters is 0.8h+16. We can see that at this time lift is going above the ground as it has a positive slope.

The travel time it takes elevator B to reach height h in meters is - 0.8h+12 seconds. We can see that at this time lift B is going below the ground as it has a negative slope.

To find the time it would take for each elevator to reach ground level at the given time, we equate the time taken by both the elevators,

0.8h+16=-0.8h+12

1.6h=-4

h=-2.5

Thus, height of each elevator = -2.5m

If the two elevators travels towards one another, the height at which they pass each other will be (because one is going up an one is going down) = -2.5m.

Time taken by the elevator A to reach the height - 2.5 is : 0.8 (-2.5) + 16=14 seconds.

Time taken by the elevator B to reach the height - 2.5 is: - 0.8 (-2.5) + 12=14 seconds.

If we are on an underground parking level 14 meters below ground, then Time taken by elevator A will be=0.8 (-14) + 16=-11.2+16=4.8 seconds and time taken by elevator B will be=-0.8 (-14) + 16=11.2+16=27.2 seconds.

Since, time taken by elevator A is less than time taken by elevator B, then elevator A will reach first.