**Shortcut 55:**

Train crossing a man on another train in same direction

* [latex]T=\frac{L_T}{S_1\sim S_2} [/latex]*

Question:

Two trains A and B of length 100m and 200 are travelling at a speed of 72kmph and 54kmph respectively in same directions. How long will train A take to cross a man travelling in train B?

Answer:

LT = 100, (Length of train crossing the man)

S1 = 72kmph = 72(5/18)mps = 20mps

S2 = speed of the man travelling in train B

S2 = 54kmph = 36(5/18)mps = 10mps

Substitute the values in the above formula, we get

T = (100)/(20-10)

= 10 seconds

**Shortcut 56:**

Time taken to meet from different stations

* [latex]T=\frac D{S_1+S_2} [/latex]*

Question:

Two trains A and B start from stations 1 and 2, 300km apart at 9am and travel towards each other at a speed of 30kmph and 50kmph respectively. At what time they will meet?

Answer:

D = 300km

S1 = 30kmph; S2 = 50kmph

T = 300/(30+50)

= 3.75 hours

= 3 hours 45 minutes

The time at which the two trains will meet is,

= 9am + 3:45 hours

= 12:45pm

**Shortcut 57:**

Time taken for trains to meet in same direction

* [latex]T=\frac D{S_1\sim S_2} [/latex]*

Train A starts from station at 10am at a speed of 50kmph. Train B starts from the same station at 11am at a speed of 55kmph. How long will train B take to meet train A?

Answer:

Difference in time of starting between the two trains = 11am – 10am = 1 hour

Distance travelled by train A in 1 hour = 1 x 50

= 50km

D = 50, distance between two trains

S1 = 50; S2 = 55

T = 50/(55 – 50) = 10 hours

The two trains will meet at 11am + 10 hours

= 9pm

**Shortcut 58:**

Speed ratio

* [latex] S_1:S_2=\sqrt a:\sqrt b[/latex]*

a, b – time taken by respective trains travelling in opposite direction, to reach destination after they meet.

Question:

Two trains start from stations A and B. Speed of train from A is 60kmph. The two trains meet each other and take 9 and 4 hours to reach the destined stations. What is the speed of train from B?

Answer:

a = 9 hours

b = 4 hours

S1 = 60kmph

S1 : S2=√9 : √4

60 : S2 = 3 : 2

S2 = 40 kmph