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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**

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