Question 4 the day - Question 4 the day Train A traveling...

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Question 4 the day: April 29, 2002 Train A traveling at 60 km/hr leaves Mumbai for Delhi at 6 P.M. Train B traveling at 90 km/hr also leaves Mumbai for Delhi at 9 P.M. Train C leaves Delhi for Mumbai at 9 P.M. If all three trains meet at the same time between Mumbai and Delhi, what is the speed of Train C if the distance between Delhi and Mumbai is 1260 kms? (1) 60 km/hr (2) 90 km/hr (3) 120 km/hr (4) 135 km/hr Correct Answer - (3) Solution: All three trains meet at the same time between Delhi and Mumbai. Which means Train A and Train B are at the same point at that time. This will happen when Train B is overtaking Train A. Train A starts 3 hours before Train B. Therefore, by the time Train B leaves Mumbai, Train A has covered 3 * 60 = 180 kms. The relative speed between Train A and Train B = 90 - 60 = 30 kmph. Therefore, Train B will overtake Train A in = 6 hours from the time Train B leaves Mumbai. That is at 3 A.M, Train B will overtake Train A. The point between Mumbai and Delhi at which Train B overtakes Train A will be 6*90=540 kms from Mumbai. Train C will also be at that point at 3 A.M while Train B is overtaking Train A. And Train C would have travelled 1260-540 = 720 kms in these 6 hours. Therefore, the speed of Train C = = 120 km/hr. As far as Speed, Time and Distance chapter is concerned, you need to know exactly three basic concepts. Concept 1: Distance = Speed * Time Just ensure that the units that you use are all in sync with each other. That is if you are measuring speed in km/hr, then make sure that the distance is calculated in km and time in hours. Else convert the units appropriately. Concept 2:
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Average Speed = Total Distance Traveled Total Time Taken Concept 3: Relative Speed of two objects moving at speeds S 1 and S 2 in the same direction = | S 1 - S 2 | Relative Speed of two objects moving at speeds S 1 and S 2 in opposite directions = S 1 + S 2 Question Two trains, 200 and 160 meters long take a minute to cross each other while traveling in the same direction and take only 10 seconds when they cross in opposite directions. What are the speeds at which the trains are traveling? (1) 21 m/s; 15 m/s (2) 30 m/s; 24 m/s (3) 18 m/s; 27 m/s (4) 15 m/s; 24 m/s Correct Answer - (1) Solution The distance covered by the two trains when they cross each other completely = sum of the length of both the trains. Distance covered = 200 + 160 = 360 meters. Let Train 1 be traveling at S 1 m/sec and Train 2 be traveling at S 2 m/sec. When the trains are traveling in the same direction, their relative speeds = | S 1 - S 2 | m/sec. When the trains are traveling in opposite directions, their relative speeds = S 1 + S 2 m/sec. The relative speeds of the train when they are traveling in the same direction = = = 6 m/sec = S 1 - S 2 –- (1) The relative speed when the trains are traveling at opposite directions = = = 36 m/sec = S 1 + S 2 . –- (2) Solving eqn (1) and eqn (2) we get S 1 = 21 m/sec and S 2 = 15 m/sec.
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  • Spring '15
  • Savadi
  • Scalar, Speed of sound, Velocity, Miles per hour, Trains

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