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An elevator goes down at the rate of 4 m per minute. If it starts going down from a height of 15 m above the ground level, find the time taken by the elevator to reach 165 m below the ground level.
(Consider the distance above the ground level to be a positive integer and that below the ground level by a negative integer)
Given: An elevator goes down at the rate of 4 m per minute
It starts going down from a height of 15 m above the ground level
To do: Find the time taken by the elevator to reach 165 m below the ground
level.
Answer:
Rate of the descent of elevator = 4m/min
Height of the starting point of descent = 15 m
Distance below ground level taken as negative and above ground as positive.
Position of the elevator after 1 minute after starting of descent
= $15 - 1\times 4= 15 - 4 = 11$m
Position after n minutes = $15 - n \times 4 = 15 - 4n$
Time taken to reach a depth of -165
$15 - 4n = - 165$
$4n = 15 + 165 = 180$ or n = $\frac{180}{4}$ = 45 minutes