Question

A 4000m long train takes 36 sec. To cross a man walking at 20km /hr in the direction opposite to that of the train. What is the speed of train?

Answer 1

Given :–

• Speed = 4000m
• Time = 36s
• Speed of man = 20km/hr

To Find :–

• Speed of the train.

Solution :–

For finding the speed of the train,

We use,

$\sf \frac{4000}{36}$ – speed of man

First, we have to convert speed of man km/hr into m/s, because speed of train is in the m/s.

Do converting km/h to m/s, we need to divide the value of speed by 3.6.

I.e., $\frac{speed \: of \: man}{3.6}$

So,

• Speed of man = 20km/hr

→ $\frac{20}{3.6}$

→ $\frac{20 \times 10}{36}$

→ $\frac{\cancel{200}}{\cancel{36}}$

→ $\frac{\cancel{100}}{\cancel{18}}$

→ $\frac{50}{9}$

→ 5.556m/s

• Speed of man = 5.556m/s

Now,

→ $\frac{4000}{36}$ – 5.556 m/s

→ $\frac{4 \cancel{000}}{36} - \frac{5556}{1\cancel{000}}$

After cancel the zeros, we obtain

→ $\frac{\cancel4}{\cancel{36}} - 5556$

Cut the denominator (4) and the numerator (36) by 2, we obtain

→ $\frac{2}{18} - 5556$

Again cut the denominator (2) and the numerator (18) by 2, we obtain

→ $\frac{1}{9} - 5556$

→ $\frac{5556}{9}$

→ 617.33m/s

Now, convert m/s to km/hr.

For converting multiply the value of m/s by 18/5,

So,

→ 617.33 × $\frac{18}{5}$

→ 2,222.388km/hr.