A man in a train traveling at 30 km/hr notices that a train going in the opposite direction passes him in 9 seconds. If the length of this train is 200m, find its speed?

Question

anonymous · Answer

solve 
$$200=(30+r)9$$ for r

anonymous · Answer

distance=rate x time

The train's relative speed is 200/9 m/s=80 km/hr
Speed=80-30=50 km/hr

siddharth · Answer

Let the other train's speed be v km/hr. Now, if we consider the man to be stationary (his frame of reference), the other train will be travelling at 30+v km/hr in the opposite direction. 

So, other train travels 200m in 9 seconds.

Distance = speed * time
200/1000 km = (30+v) km/hr * 9/3600 hrs

20 = (30+v)/4

v = 50 km /hr

anonymous · Answer

Hello, siddharth, but 200/1000 is 0.2

siddharth · Answer

I did some simplification:

$$\frac{200}{1000} = \frac{9(30+v)}{3600}$$
multiply both sides by 1000:
$$200 = \frac{9(30+v)}{3600} \times 1000$$
$$200 = \frac{9(30+v)}{36} \times 10$$
divide both sides by 10
$$20 = \frac{9(30+v)}{36} $$