Trains 4 8 5

7x4 + 9x6 82 , 1 the required time = ~ - -> seconds. 7 + 9 16 8

Exercise 1. Two trains are moving in the opposite directions on par-allel tracks at the speeds of 64 km/hr and 96 km/hr re-

spectively. The first train passes a telegraph post in 5 seconds whereas the second train passes the post in 6 seconds. Find the time taken by the trains to cross each other completely.

18 28 a) sec b) sec c) 6 sec d) None of these The speeds of two trains are in the ratio of 3 :5. They are moving on the opposite directions on parallel tracks. The first train crosses a telegraph pole in 3 seconds whereas the second train crosses the pole in 5 seconds. Find the time taken by the trains to cross each other completely.

15 A 1 b)4sec c) sec d) 4-17 a) sec

sec 3. The speeds of two trains are in the ratio of 2 :3 . They are moving on the opposite directions on parallel tracks. The first train crosses a telegraph pole in 10 seconds whereas the second train crosses the pole in 15 sec-onds. Find the time taken by the trains to cross each other completely. a) 23 sec b) 14 sec c) 13 sec d) 16 sec

4. The speeds of two trains are in the ratio 5 : 9. They are going in opposite directions along parallel tracks. If each takes 5 seconds to cross a telegraph post, find the time taken by the trains to cross each other completely? a) 3 sec b)5 sec c)6 sec d)9 sec

Answers l.b;Hint:x:y = 64:96 = 2 :3

Now applying the given rule, we have the required answer: : a 3.c 4.b

2x5+3x6 2 + 3

28 3 = T = 5 J S e c

Rule 36 Theorem: A train with x km/hr crosses a bridge in Tsec-onds. Another train L metres, shorter crosses (fee same bridge at y km/hr. Time taken by the second train to cross the

bridge is given by X-T-yx 18

seconds.

Illustrative Example Ex.: A train with 90 km/hr crosses a bridge in 36 seconds.

Another train 100 metres shorter crosses the same

bridge at 45 km/hr. Find the time taken by the second train to cross the bridge.

Soln: Detail Method: Speed of the first train = 90 x = 25 rn/sec

I o Let the length of the bridge be x m and length of the train be y m. or,x+j>=25 x 36metres ...(i) mis. ami imsfr. hits M Q! ft Speed of the second train = 4J * = m/sec

25 x + (y100) = ~^~x ' (ii) [where t = required time] Now, putting equation (i) into equation (ii), we have,

25t (25x36)-100 =

or, / = (900-100)2 800x2 - 6 4 seconds.

2.

25 25 Quicker Method: Applying the above theorem, we have the required time

= ~ x 3 6 - - ^ - = 7 2 - 8 = 64 sees. 45 45x5 18

Exercise 1. A train with 60 km/hr crosses a bridge in 25 seconds.

Another train 120 metres shorter crosses the same bridge at 30 km/hr. Find the time taken by the second train to cross the bridge. a) 35 sec b) 34.6 sec c) 35.2 sec d) 35.6 sec A train with 36 km/hr crosses a bridge in 18 seconds. Another train 90metres shorter crosses the same bridge at 27 km/hr. Find the time taken by the second train to cross the bridge. a) 20 sec b) 18 sec c) 16 sec d) 12 sec A train with 72 km/hr crosses a bridge in 36 seconds. Another train 180 metres shorter crosses the same bridge at 54 km/hr. Find the time taken by the second train to cross the bridge. a) 24 sec b) 32 sec c) 36 sec d) Can't be determined

Answers l.d 2.d 3.c

Miscellaneous 1. Train 'A' leaves Mumbai Central for Lucknow at 11 am,

running at the speed of 60 km/hr. Train 'B' leaves Mumbai Central for Lucknow by the same route at 2 pm on the same day, running at the speed of 72 km/hr. At what time

3.

486 PRACTICE BOOK ON QUICKER MATHS will the two trains meet each other?

[BSRBPatnaPO,2001] a) 2 am on the next day b) 5 am on the next day c) 5 pm on the next day d) None of these

2. A passenger train leaves Calcutta at 4 PM and travels at the rate of 30 kilometres an hour. The mail train leaves Calcutta at 9 PM and travels, on a parallel line of rails, at the rate of 45 km an hour, when will the second train overtake the first? a) 10 hrs after the first train start b) 12 hrs after the second train starts c) 10 hrs after the second train starts d) 12 hrs after the first train starts

Answers 1. b; Distance covered by train A before the train B leaves

Mumbai Central = 60 x 3 = 180 km

.-. Time taken to cross each other = = 15 hrs 12

.-. required time = 2 pm + 15 hours = 5 am on the next day.

2. c; Hint: The first train has started 5 hrs before the sec-ond. Therefore, (30 x 5 = 150) km away when the sec-ond train starts. Therefore the second train has to gain 150 km on the first, at the rate of 15 ie (45 - 30 = 15) km an hour. Second train gains 15 km in 1 hour on the first. .-. Second train gains 150 km in 10 hours on the first. .". the time required is 10 hours after the second train starts. .-. the second overtakes the first at a distance of

(45 x 10)=450 km from Calcutta.