Question

19. A train travelling at the speed of 36 km/h crosses a 98-m-long platform in 20 s. Find
the length of the train.​

Answer 1

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Let the length of train be x.

Total distance traveled = Length of train + Length of bridge = 98 + x

Time taken = 20 seconds

Speed = 36 km/h or 10m/s

Speed = Total distance traveled / Time taken

Or

10 = (98 + x) / 20 (Substituting the values)

10 × 20 = 98 + x

x = 102 m

Answer 2

Given :-

Speed of the train = 36 km/hr

Time taken = 20 s

Length of the platform = 98 m

To Find :-

The length of the train.​

Analysis :-

Since the time and the length are in seconds and meters, firstly we have to convert km/hr to m/s.

Then find the distance traveled using it's respective formula.

At last, subtract the distance traveled from the length of the platform in order to get the length of the train.

Solution :-

We know that,

• t = Time
• s = Speed
• l = Length

Since the time and the length are in seconds and meters, we have to convert km/hr to m/s.

Given that,

Speed of train = 36 km/hr

By converting,

$\sf 36 \times \dfrac{18}{5}$

$\sf =10 \ m/s$

By the formula,

$\underline{\boxed{\sf Total \ distance=Total \ speed \times Total \ time}}$

Given that,

Time taken (t) = 20 s

Speed (s) = 10 m/s

Substituting their values,

Distance = 20 × 10

Distance = 200 m

According to the question,

Given, Length of the platform = 98 m

Length of train = Distance travelled - Length of platform

By substituting,

Length of train= 200 - 98

Length = 102 m

Therefore, the length of the train is 102 m.