 Two trains cross each other in 14 sec when they are moving in the opposite direction, and when they are moving in the same direction they cross each other in 3 minute2 sec. Find the speed of the faster train by what percent more than the speed of the slower train?
Here we will learn about the concept of two trains passes in the opposite direction. When two train passes a moving object (having some length) in the opposite direction Let length of faster train be l meters and length of slower train be m meters Let the speed of faster train be x km/hr Relative speed = (x + y) km/hr. Then, time taken by the faster
train to pass the slower train = (l
+ m) meters/(x + y) km/hr Now we will learn to calculate when two trains running on parallel tracks (having some length) in the opposite direction. Solved examples when two trains passes (having some length) in the opposite direction: 1. Two trains of length 150 m and 170 m respectively are running at the speed of 40 km/hr and 32 km/hr on parallel tracks in opposite directions. In what time will they cross each other? Solution: Relative speed of train = (40 + 32) km/hr = 72 km/hr = 72 × 5/18 m/sec = 20 m/sec Time taken by the two trains to cross each other = sum of length of trains/relative speed of trains = (150 + 170)/20 sec = 320/20 sec = 16 sec Therefore, the two trains crossed each other in 16 seconds. 2. Two trains 163 m and 187 m long are running on parallel tracks in the opposite directions with a speed of 47 km/hr and 43 km/hr in. How long will it take to cross each other? Solution: Relative speed of train = (47 + 43) km/hr = 90 km/hr = 90 × 5/18 m/sec = 25 m/sec Time taken by the two trains to cross each other = sum of length of trains/relative speed of trains = (163 + 187)/25 sec = 350/25 sec = 14 sec Therefore, the two trains crossed each other in 14 seconds. Speed of Train Relationship between Speed, Distance and Time Conversion of Units of Speed Problems on Calculating Speed Problems on Calculating Distance Problems on Calculating Time Two Objects Move in Same Direction Two Objects Move in Opposite Direction Train Passes a Moving Object in the Same Direction Train Passes a Moving Object in the Opposite Direction Train Passes through a Pole Train Passes through a Bridge Two Trains Passes in the Same Direction Two Trains Passes in the Opposite Direction 8th Grade Math Practice From Two Trains Passes in the Opposite Direction to HOME PAGE
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Concept: When a train of length ‘l1’ metres running with speed ‘s1’ km/hr crosses another train of length ‘l2’ running with a speed of ‘s2’ in opposite direction in ‘t’ seconds : (l1 + l2) = (s1 + s2) × t When a train of length ‘l1’ metres running with speed ‘s’ km/hr crosses a bridge or a platform of length ‘l2’ in ‘t’ seconds: (l1 + l2) = s × t × (5/18) Calculations: Let the length of first train be l1 Speed of first train be s1 = 5x Length pf second train be l2 Speed of second train be s2 = 2x ∴ (l1 + l2) = (s1 + s2) × t ⇒ (l1 + l2) = (5x + 3x) × 14 = 112x ----(i) Now the faster train crosses the platform of 190 m in 20 sec ⇒ (l1 + 190)/5x = 20 ⇒ (l1 + 190) = 100x ⇒ l1 = 100x – 190 The slower train crosses a 290 m long platform in 36 sec ⇒ (l2 + 290)/3x = 36 ⇒ (l2 + 290) = 108x ⇒ l2 = 108x – 290 ∴ l1 + l2 = 100x – 190 + 108x – 290 = 208x – 480 ----(ii) Equating (i) and (ii) ⇒ 208x – 480 = 112x ⇒ 96x = 480 ⇒ x = 5 ∴ s1 = 5 × 5 = 25 m/s, s2 = 3 × 5 = 15 m/s l1 = 500 – 190 = 310, l2 = 540 – 290 = 250 ∴ Time taken by both the trains to cross each other when they are 240 m apart ⇒ (l1 + l2 + 240)/(s1 + s2) = t ⇒ (310 + 250 + 240)/(25 + 15) = t ⇒ 800/40 = 20 sec India’s #1 Learning Platform Start Complete Exam Preparation
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