A train leaves New Delhi for Ludhiana, 324 km away, at 9 a.m. One hour later, another train leaves Ludhiana for New Delhi. They meet at noon. If the second train had started at 9 a.m. and the first train at 10.30 am., they both would still have met at noon. Find the speed of each train.
Linear Equations
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Question

A train leaves New Delhi for Ludhiana, 324 km away, at 9 a.m. One hour later, another train leaves Ludhiana for New Delhi. They meet at noon. If the second train had started at 9 a.m. and the first train at 10.30 am., they both would still have met at noon. Find the speed of each train.

Linear Equations

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KnowledgeBoat · Accepted Answer

Let the speed of the first train be u km/hr and that of the second train be v km/hr. The total distance between New Delhi and Ludhiana is 324 km. For the first case: The first train starts at 9:00 a.m. and meets the second train at 12:00 p.m. Time taken by 1st train = (12 - 9) = 3 hrs The second train starts at 10:00 a.m. and meets the first train at 12:00 p.m. Time taken by 2nd train = (12 - 10) = 2 hrs We know that, distance = speed x time ⇒ 3u + 2v = 324 ....................(1) For the second case: The first train starts at 10:30 a.m. and meets the second train at 12:00 p.m. Time taken by 1st train = (12 - 10:30) = 1.5 hrs The second train starts at 9:00 a.m. and meets the first train at 12:00 p.m. Time taken by 2nd train = (12 - 9) = 3 hrs ⇒ 1.5u + 3v = 324 ....................(2) Multiply equation (1) by 3 and equation (2) by 2, we get: ⇒ (3u + 2v = 324) x 3 ⇒ 9u + 6v = 972 ....................(3) And, (1.5u + 3v = 324) x 2 ⇒ 3u + 6v = 648 ....................(4) Now, subtract equation (4) from equation (3): ⇒ u = 54 Substituting the value of u in equation (1), we get: ⇒ 3 54 + 2v = 324 ⇒ 162 + 2v = 324 ⇒ 2v = 324 - 162 ⇒ 2v = 162 ⇒ v = = 81 Hence, the speed of the first train is 54km/hr and the speed of the second train is 81km/hr.

Mathematics

A train leaves New Delhi for Ludhiana, 324 km away, at 9 a.m. One hour later, another train leaves Ludhiana for New Delhi. They meet at noon. If the second train had started at 9 a.m. and the first train at 10.30 am., they both would still have met at noon. Find the speed of each train.

Linear Equations

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