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# A train crosses a bridge of length 500 m in 40 seconds and a lamp post

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Math Expert
Joined: 02 Sep 2009
Posts: 43896
A train crosses a bridge of length 500 m in 40 seconds and a lamp post [#permalink]

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18 Aug 2015, 01:27
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A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Joined: 21 May 2013
Posts: 581
Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post [#permalink]

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18 Aug 2015, 02:32
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

Let Length of train=LT
Speed of train=VT

Time taken =(Length of train +Length of Bridge)/Speed of Train
40=(LT+500)VT
And, LT/VT=15
Put LT/VT=15 in the first equation,
15+500/VT=40
VT=20
Using value of VT=20, LT=300M
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Joined: 08 Sep 2012
Posts: 66
Location: India
Concentration: Social Entrepreneurship, General Management
WE: Engineering (Investment Banking)
Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post [#permalink]

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18 Aug 2015, 03:19
1
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Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

Length of train = L
Speed of train = S

(L+500) = S*40
L = S*15 => S = (L / 15)

=> L+500 = (L / 15) * 40
=> L = 300m

Option E
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Joined: 08 Jul 2010
Posts: 1958
Location: India
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Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post [#permalink]

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18 Aug 2015, 06:10
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Expert's post
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

Let Length of Train = L

Case-1: Distance = 500+L (While crossing the bridge)
Time = 40 Seconds
i.e. Speed = Distance / Time = (500+L)/40

Case-2: Distance = L (While passing the lamp post)
Time = 15 Seconds
i.e. Speed = Distance / Time = (L)/15

But Since speed has to be same in both cases so

(500+L)/40 = (L)/15

i.e. 8L = 3L + 1500
i.e. 5L = 1500
i.e. L = 300

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Manager
Joined: 10 Jun 2015
Posts: 126
A train crosses a bridge of length 500 m in 40 seconds and a lamp post [#permalink]

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18 Aug 2015, 06:39
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

let the length of the train is L
L/15 = (L+500)/40
solving, L=300
Manager
Joined: 14 Mar 2014
Posts: 148
GMAT 1: 710 Q50 V34
Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post [#permalink]

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18 Aug 2015, 20:56
1
KUDOS
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

IMO: E

Speed = $$\frac{Distance}{time}$$

Let Length of train be $$L_T$$
Let Length of Bridge be $$L_B$$
Speed of train be S

While crossing Lamp post
S = $$\frac{L_T}{15}$$
$$L_T$$ = 15S --(i)

While crossing Bridge
s = $$\frac{L_T + L_B}{40}$$
40s = $$L_T$$+$$L_B$$
40s = 15s+500 (from eq--(i) & given length of bridge = 500)
s= 20

Sub in eq-(i) we get $$L_T$$ = 300
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Retired Moderator
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Location: Switzerland
Concentration: Economics, Finance
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A train crosses a bridge of length 500 m in 40 seconds and a lamp post [#permalink]

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21 Oct 2015, 10:36
1
KUDOS
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

Kudos for a correct solution.

You have two concepts covered in this topic: a train which crosses a stationary object with (1) and without (2) length:

Crossing a stationary object with length (bridge = 500m):

r * t = Length of Train + Length of object ->> Where r = spdeed and t = time

In this question we get: 40r = 500 + Length of Bridge

then crossing a stationary object without length/with negligible length:

r*t = Length of train

So we have 15r = Length of Train ->> plug in above to get:

40r = 500 + 15r
25r = 500
r = 20

Plug in r = 20 in 15r = Length of train to get Length = 300.
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Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post [#permalink]

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19 May 2017, 05:31
Bunuel wrote:
A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?

A. 375 m
B. 750 m
C. 250 m
D. 800 m
E. 300 m

We can let x = the length of the train in metres. To cross the 500-m bridge in 40 seconds, the head of the train must enter at one end of the bridge and the tail of the train must exit from the other end of the bridge. Therefore, in 40 seconds, the train actually travels the length of the bridge plus the train’s body length. In other words, the train travels (500 + x) metres in 40 seconds. If we let r be the speed of the train, we have:

500 + x = 40r

Since there are two unknowns, we need another equation in order to solve for x. We will use the fact that the train crosses a lamp post on the bridge in 15 seconds. This means that after the head of the train first crosses the lamp post, it takes 15 seconds for the train’s tail to cross the lamp post too. In other words, the train travels a distance equal to its body length in 15 seconds. So, we have:

x = 15r

Substitute x = 15r in the first equation and we have:

500 + 15r = 40r

500 = 25r

20 = r

So, we know the speed of the train is 20 m/s and its body length is x = 15r = 15(20) = 300 metres.

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Re: A train crosses a bridge of length 500 m in 40 seconds and a lamp post   [#permalink] 19 May 2017, 05:31
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