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Bunuel
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A new skyscraper has 172 floors. Tom is in an elevator on the 169th 28 Aug 2020, 00:25
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A new skyscraper has 172 floors. Tom is in an elevator on the 169th floor going down at a rate of 16 floors per minute and James is in an elevator on the 13th floor going up at a rate of 10 floors per minute. If Tom and James make no stops along the way, what floor will they meet on?

A. 43
B. 60
C. 73
D. 96
E. 110
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C
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A new skyscraper has 172 floors. Tom is in an elevator on the 169th Updated on: 31 Aug 2020, 19:57
Originally posted by RaghuveerTR on 28 Aug 2020, 00:47.
Last edited by RaghuveerTR on 31 Aug 2020, 19:57, edited 1 time in total.
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At the floor they both meet, the sum of the floors both has crossed will be 156(difference between 169 and 13)

We have the rates of each person as 16fpm and 10fpm.

d = v*t

16t + 10t = 156
t=6.. they meet after 6 minutes

By that time, Tom would've come down by 96 floors at 16fpm and James would've gone up by 60 floors.

So, they will meet at the 73rd floor.

Option C..

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A new skyscraper has 172 floors. Tom is in an elevator on the 169th 28 Aug 2020, 01:00
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Tom and James elevator speed is 16 floors/min and 10 floors/min

Distance between floors = 169-13 (Tom floor-James floor)
= 156
Speed = 16+10 = 26 (moving in each other direction).
So they will meet after = 156/26 = 6min later

James will be on 73rd floor (13+60) after 6 min
Tom will be on 73rd floor (169-96) after 6 min

Answer is C

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A new skyscraper has 172 floors. Tom is in an elevator on the 169th 28 Aug 2020, 01:18
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total floors 172
relative speed is 16+10 ; 26 floors per minute
and net ∆ b/w Tom & James ; 169-13 ; 156
so they meet after 156/26 ; 6 mins
i.e in 6 mins Tom is at 6*16 ; 96 ; 169-96 ; 73rd floor
also James 10*6 ; 60 +13 ; 73 rd floor
OPTION C

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A new skyscraper has 172 floors. Tom is in an elevator on the 169th floor going down at a rate of 16 floors per minute and James is in an elevator on the 13th floor going up at a rate of 10 floors per minute. If Tom and James make no stops along the way, what floor will they meet on?

A. 43
B. 60
C. 73
D. 96
E. 110
­
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A new skyscraper has 172 floors. Tom is in an elevator on the 169th 28 Aug 2020, 01:27
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Distance between Tom & James = 169-13 = 156 floors
Relative speed = 13+ 10 = 26 floors/min
time required to meet = 156/26 = 6 min
Floor reached by James after 6min = 13th floor + (6*10) floors = 73rd Floor

(C) correct answer
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A new skyscraper has 172 floors. Tom is in an elevator on the 169th 28 Aug 2020, 05:21
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Bunuel
A new skyscraper has 172 floors. Tom is in an elevator on the 169th floor going down at a rate of 16 floors per minute and James is in an elevator on the 13th floor going up at a rate of 10 floors per minute. If Tom and James make no stops along the way, what floor will they meet on?

A. 43
B. 60
C. 73
D. 96
E. 110
 
Here the time traveled by both Tom & James should be the same.

Time is taken by Tom=T1
Time is taken by James=T2

\(T1=T2\)

\(\frac{S1}{V1}=\frac{S2}{V2}\) (since \(Speed(V)= \frac{Distance(S)}{Time(T)}\))

\(\frac{S1}{16}=\frac{S2}{10}\)

\(\frac{S1}{S2}=\frac{16}{10}=\frac{8}{5}\\
\)

the total difference in Floor=\(169-13=156\)

\(8x+5x=156\)
\(x=12\)

the floor where they meet=\(13+5*x= 13+5*12=73\)­
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A new skyscraper has 172 floors. Tom is in an elevator on the 169th 24 Jul 2022, 01:34
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Bunuel
A new skyscraper has 172 floors. Tom is in an elevator on the 169th floor going down at a rate of 16 floors per minute and James is in an elevator on the 13th floor going up at a rate of 10 floors per minute. If Tom and James make no stops along the way, what floor will they meet on?

A. 43
B. 60
C. 73
D. 96
E. 110


Let's visualize this problem; see attached image.

Attachment:
File comment: Visual representation
Untitled.png
Untitled.png [ 7.65 KiB | Viewed 3314 times ]

The problem statement points to which floor they meet on. We know both elevators will meet at the same time, hence we use the time as the subject of the formula.

Time taken by elevator starting from floor 13: \(t\) = \(\frac{x}{10}\) - (1)

Time taken by elevator starting from floor 169: \(t\) = \(\frac{156-x}{16}\) - (2)

Since they meet at the same time, (1) = (2). Therefore,

\(\frac{x}{10}\)=\(\frac{156-x}{16}\)

\(x\) = \(60\)

But x is the number of floors above floor 13.

Hence, both elevators meet at floor \(x + 13 = 60 + 13 = 73\)

Answer choice (C) is correct.

Here's a little donut for you: Why do we have the variable \(156-x\) as part of (2)?
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A new skyscraper has 172 floors. Tom is in an elevator on the 169th 24 Jul 2022, 18:50
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Bunuel
A new skyscraper has 172 floors. Tom is in an elevator on the 169th floor going down at a rate of 16 floors per minute and James is in an elevator on the 13th floor going up at a rate of 10 floors per minute. If Tom and James make no stops along the way, what floor will they meet on?

A. 43
B. 60
C. 73
D. 96
E. 110


We can also Plug In The Answers (PITA). I usually like trying B or D, but we can notice right away that 73 makes the math super easy for James. He starts on the 13th and ends up on the 73rd. That takes 6 minutes. Tom goes 16 per minute, so 96 in 6 minutes. Is 96 the difference between 73 and 169? Yep.

Answer choice C.


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A new skyscraper has 172 floors. Tom is in an elevator on the 169th 13 Mar 2023, 15:52
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If two trains (objects, in this case Tom & James), are heading towards each other, at speeds S1 & S2 respectively, the time they meet "T" is defined as T = (Distance/ (S1+S2))


With respect to this example, the distance is D is 169- 13 = 156
T = 156/(10+16) = 6 mins

James is at 13th floor, and in 6 mins he can move 60 floors, 13+60 = 73rd floor is where they meet

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A new skyscraper has 172 floors. Tom is in an elevator on the 169th 13 Mar 2023, 22:29
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Bunuel
A new skyscraper has 172 floors. Tom is in an elevator on the 169th floor going down at a rate of 16 floors per minute and James is in an elevator on the 13th floor going up at a rate of 10 floors per minute. If Tom and James make no stops along the way, what floor will they meet on?

A. 43
B. 60
C. 73
D. 96
E. 110
 
This question is based on the concept of relative speed.
Time taken to meet = Distance between them/Relative speed
Distance between them = 169 - 13 = 156 floors
Relative speed = 16 fpm + 10 fpm = 26 fpm (since they are going in opposite directions, we add their speeds)

Time taken to meet = 156/26 = 6 mins

No of floors covered by James in 6 min = 10 *6 = 60 floors.
So at this time, James is on 13 + 60 = 73rd floor.

Answer (C)

Check this video for when to use relative speed: https://youtu.be/wrYxeZ2WsEM­
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A new skyscraper has 172 floors. Tom is in an elevator on the 169th 28 Dec 2023, 10:47
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Distance : 169-13=156
Rate : 16+10=26
Average : 156/26 = 6
I got lost here and decided to do a trial an error.
Its not B or D cause its divisible by 6 and your answer should be a minus of 13 or 169. I cant find a way to relate D here. So we're down to A and C. Looking at the ratio 10/16 --- 5=8, the distance should be closer to the middle and should be more than half the distance of 169. Settled on C. Also played with the figures and C made sense.
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