SOLUTION: In a tall office building, one elevator leaves the third floor and ascends at a speed of 2 floors per second. Another elevator leaves the 59th floor at exactly the same moment and

Question 176494: In a tall office building, one elevator leaves the third floor and ascends at a speed of 2 floors per second. Another elevator leaves the 59th floor at exactly the same moment and descends at a speed of 2 floors per second. If the two elevators do not stop, how long will it take them to pass each other? At what floor will the elvators pass each other?
I can solve this problem by subtracting 3 from 59 to get a distance of 56 floors. Since they are traveling at the same rate divide this by 2 and get 23 floors. So they would pass at the 26th floor. 23 floors at 2 floors per second would be 11.5 seconds.
My problem is that I can do all this logically but my teacher wants an equation with variables! Not sure how to do that. Thanks for any help!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a tall office building, one elevator leaves the third floor and ascends at a speed of 2 floors per second. Another elevator leaves the 59th floor at exactly the same moment and descends at a speed of 2 floors per second. If the two elevators do not stop, how long will it take them to pass each other? At what floor will the elvators pass each other?
-----------------------
Ascending DATA:
rate = 2 fpsecond ; distance = x floors ; time = d/r = x/2 seconds
--------------------------
Decending DATA:
rate = 2 fpsecond ; distance = (56-x) floors ; time = d/r = (56-x)/2 seconds
---------------------------
Equation:
time = time
x/2 = (56-x)/2
x = 56-x
2x = 56
x = 28 (# of floors each elemator moves)
---------------------------------------------
Ascending: 3 + 28 = 31st floor
Decending: 59- 28 = 31st floor
=========================================
Cheers,
Stan H.
RELATED QUESTIONS
An office building has 33 floors, each 10 feet high, and elevators that travel at a... (answered by ankor@dixie-net.com)

Suppose you find yourself in an elevator that is only capable of going up 5 floors at a... (answered by josmiceli)

Three people enter a main floor elevator of the Mathematical Sciences Building. Assuming... (answered by Edwin McCravy)

Suppose you enter an elevator at a certain floor. The elevator moves up 6 floors, down 4... (answered by ankor@dixie-net.com)

Suppose you enter an elevator at a certain floor. The elevator moves up 6 floors, down 4... (answered by algebrahouse.com)

Steve gets on the elevator at the 11th floor of the building and rides up at a rate of 57 (answered by Edwin McCravy)

An old woman entered an elevator of a five-star hotel and wished to reach the ground... (answered by josmiceli)

the elevator of a building is 10 feet above ground level on the first floor. the... (answered by ikleyn)

Tom gets on the elevator at the 11th floor and rides up at a rate of 57 floors per... (answered by ankor@dixie-net.com)