SOLUTION: An elevator went from the bottom to the top of a 240 m tower, remained there for 12 s, and returned to the bottom in an elapsed time of 2 min. If the elevator traveled 1 m/s faste
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Question 72144This question is from textbook Algebra and Trigonometry: Structure and Method
: An elevator went from the bottom to the top of a 240 m tower, remained there for 12 s, and returned to the bottom in an elapsed time of 2 min. If the elevator traveled 1 m/s faster on the way down, find its speed going up.
This question is from textbook Algebra and Trigonometry: Structure and Method
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An elevator went from the bottom to the top of a 240 m tower, remained there for 12 s, and returned to the bottom in an elapsed time of 2 min. If the elevator traveled 1 m/s faster on the way down, find its speed going up.
:
Let s = upward speed in m/sec
(s+1) = downward speed:
Distance both ways given as 240 m
:
Time = dist/speed
:
Time equation for the round trip:
time up + pause + time down = 2 min (120 sec)
= 120
:
Subtract 12 from both sides and you have:
= 108
:
Multiply equation by s(s+1) to get rid of the denominators:
240(s+1) + 240s = 108(s(s+1))
240s + 240 + 240s = 108s^2 + 108s
480s + 240 = 108s^2 + 108s
:
Arrange as a quadratic equation:
108s^2 + 108s - 480s - 240 = 0
108s^2 - 372s - 240 = 0
:
Simplify; divide equation by 12
9s^2 - 31s - 20 = 0
:
This factors to:
(9s + 5)(s - 4) = 0
:
9s = -5
s = -5/9
and
s = + 4 m/sec is the solution we want for the speed going up
:
:
Check using elapsed time for the round trip : 240/4 + 12 + 240/5 = 120 sec
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
total time = 120 - 12 sec
total time = 108 sec
r = rate going up
t = time to go up
m/sec answer
check answer
sec
OK
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