Question

How long will a boy sitting near the window of a train moving at 36 kmph see a train passing by in the opposite direction with a speed of 18 kmph . The length of the slow moving train is 90 m.

Answer 1

Given :-

Speed of the train (T₁), v₁ = 36 km/h

Speed of the train (T₂), v₂ = 18 km/h

Length of the slow-moving train = 90 m

To Find :-

Time taken by the train with speed of 18 km/h to cross the train with 36 km/h.

Analysis :-

Firstly, convert the two speed of the train from kilometer per hour to meter per second accordingly.

Then add the both speed of the train (relative speed).

Here we are given with the relative speed and the distance of the train.

In order to find the time taken by the train, substitute the values we got such that time is equal to distance divided by time.

Solution :-

We know that,

• d = Distance
• s = Speed
• t = Time

Speed is converted to m/s,

36 × 5/18 = 180/18 = 10 m/s

18 × 5/18 = 90/18 = 5 m/s

The relative speed of two bodies is the sum of the two speeds.

Relative speed,

15 + 10 = 25 m/s

Given, relative distance = 100 m

Using the formula,

$\underline{\boxed{\sf Time \ taken = \dfrac{Total \ distance}{Total \ speed} }}$

Given that,

Distance (d) = 100 m

Speed (s) = 25 m/s

Substituting their values,

⇒ t = d/s

⇒ t = 100/25

⇒ t = 4 sec

Therefore, the time taken by the train  to cross the train is 4 sec.

Additional knowledge :-

Speed:

Speed is defined as how slow or fast an object moves.

Formula: Speed = Distance/Time

In order to find the speed of an object, you shall divide the distance travelled by the time taken to cover the distance.

Speed is measured in km/h or m/s.

Distance:

Distance is defined as how far an object is from one another. Speed is directly proportional to distance and inversely proportional to time.

Formula: Distance = Speed × Time

In order to find the distance travelled by an object, you shall multiply the speed with the time taken by an object.

Distance is measured by meters, kilometers, miles or feet.

Time:

Time is defined as a measurable period. The speed increases, the time taken will decrease and vice versa.

Formula: Time = Distance/Speed

In order to find the time taken by an object, you shall divide the distance travelled by the speed of the object.

Time is measured by hours, minutes or seconds.

Answer 2

Answer:

Given :-

• Speed of train (T1) = 36 kmph
• Speed of train (T2) = 18 kmph
• Length of train = 90 m

To Find :-

Time taken by the train with speed of 18 km/h to cross the train with 36 km/h.

Solution :-

Firstly we will convert the speed in m/s

Speed of train (T1) = 36 × 5/18 = 10 m/s

Speed of Train (T2) = 18 × 5/18 = 5 m/s

Relative speed,

10 + 15 = 25 m/s

Total distance = 100 m

$\huge \boxed {\bf Time = \dfrac {Distance}{Speed}}$

$\sf \: Time \: = \dfrac{100}{25}$

$\sf \:Time \: = 4 \: sec$

Therefore, the time taken by the train to cross the train is 4 sec.

Speed :-

Speed is describe that how fast or slow the speed is.

Speed = Distance/Time

Time :-

It is a measurable period.

Time = Distance/Speed

Distance :-

It describes how far or near the object goes.

Distance = Time × Speed