Aptitude - Problems on Trains - Discussion

Length of bridge = (speed of the train * time taken to cross the bridge) - length of the train.
= ((45*5/18)*30) - 130,
=((25/2) * 30) -130,
=(750/2) - 130,
= 375m/s - 130s,
= 245m.

To find the length of the bridge, we need to calculate the distance the train travels in 30 seconds.

First, we convert the train's speed from km/hr to m/s:

Speed in m/s = (Speed in km/hr * 1000)/3600
So, the train's speed in m/s = (45 km/hr * 1000)/3600 = 12.5 m/s.

Now we can calculate the distance the train travels in 30 seconds:
Distance = Speed * Time.

Distance = 12.5 m/s * 30 s = 375 meters.

Since the train is 130 meters long, the remaining distance must be the length of the bridge:
Length of the bridge = Distance - Length of the train.

Length of the bridge = 375 m - 130 m = 245 meters.

Therefore, the length of the bridge is 245 meters.

My Question is why we should convert 45 km/hr into meters/per second which is a unit of speed instead of that we can convert 130/30 which is also equal to speed?

Anyone, explain this to me.

Solution:

45 * 5/18 = 12.5,
12.5 * 30 = 375,
375 - 130 = 245,
So, this is how we get 245.

45km In 1 hr.
45km In 60 min.
45 km In 60*60 seconds
45000m In 60*60 seconds
45000/120 In 30 seconds
375.m in 30 seconds.
375m including with train length so the train length is;
375 - 130 = 245 m ANS.

Distance travelled by Train= length of bridge + length of the train
So, x + 130m.
Speed = 45km/hr = 45 * 5/18 = 25/2 m/s.
Distance = speed * time.
25/2 * 30,
= 245m.

To convert kilometres per hour (km/hr) to meters per second (m/sec), we use the conversion factor of 5/18. This conversion factor is derived from the relationship between kilometres and meters, as well as hours and seconds.

Here's the breakdown of the conversion:

1 kilometer = 1000 meters.
1 hour = 3600 seconds.

To convert km/hr to m/sec, we need to cancel out the kilometres and hours units while retaining the meters and seconds units. We can do this by multiplying the value in km/hr by a conversion factor that equates to 1.

To convert kilometres to meters, we multiply by 1000 (since 1 kilometre is equal to 1000 meters). This step cancels out the kilometres unit.

To convert hours to seconds, we multiply by 3600 (since 1 hour is equal to 3600 seconds). This step cancels out the hours unit.

So, the conversion factor becomes:
(1000 meters/1 kilometer) * (1 hour/3600 seconds)

Simplifying this expression gives us:
(1000/1) * (1/3600) = 1000/3600 = 5/18.

Hence, multiplying the value in km/hr by 5/18 will convert it to m/sec.

Why do we take 5/18, anyone, please Explain it?

Soln,
L.t -130m ,s -45km/hr ,t -30 sec
L.b - ?.

Let us assume length of the bridge as x,
D = s* t.

130 (l.t) + x(l.b) = 45 km/hr * 30 sec.
130 + x =45 * 5/18 m/ sec * 30 sec.

After solving we will get,
130 + x = 375,
x = 375 -130,
x = 245 m.
So, the length of the bridge is 245 m.

Given TD = 130m, speed = 45km/h, Time = 30sec.
And Length of the Station = x.

speed = 45*5/18 .
=225/18.
So, the speed =25/2.

know the length of the station,
x + TD = speed * Time
x + 130 = 25/2 * 30
x + 130 = 12.5 * 30
x + 130 = 375.
x = 375 - 130,
Final x = 245.
The correct answer is option C.