# SEP01 – Problems on Trains

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Today, We are going to take a test on Problems based on Train.

Before you take the test read these posts to be comfortable.

Important Formulae

1, km/hr to m/s conversion:

a km/hr =$\left(a\;x\frac5{18}\right)$m/s.

2, m/s to km/hr conversion:

a m/s =$\left(a\;x\frac{18}5\right)$km/hr.

3,  Formulas for finding Speed, Time and Distance

(i)  Speed, Time and Distance:

Speed =$\left(\frac{Dis\tan ce}{time}\right)$ , Time = $\left(\frac{Dis\tan ce}{speed}\right)$ , Distance = (Speed x Time).

(ii) km/hr to m/sec conversion:

x km/hr =$\left(x\;x\frac5{18}\right)$m/sec.

(iii) m/sec to km/hr conversion:

x m/sec =$\left(x\;x\frac{18}5\right)$km/hr.

(iv) If the ratio of the speeds of A and B is a : b, then the ratio of the the times taken by then to cover the same distance is $\frac1a:\frac1b$or b : a.

(v) Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then,the average speed during the whole journey is $\left(\frac{2xy}{x+y}\right)$km/hr.

4,  Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres.

5, Time taken by a train of length l metres to pass a stationery object of length b metres is the time taken by the train to cover (l + b) metres.

6, Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (uv) m/s.

7, Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s.

8, If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then:

The time taken by the trains to cross each other = $\left(\frac{a+b}{u+v}\right)$sec.

9, If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then:

The time taken by the faster train to cross the slower train =$\left(\frac{a+b}{u-v}\right)$sec.

10, If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then:

(A’s speed) : (B’s speed) = $\left(\sqrt b:\sqrt a\right)$.

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#### SEP01 - Trains

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