A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But, if he travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train and the speed of the car.
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The speed of the train be x km/hr The speed of the car = y km/hr From the question, it’s understood that there are two parts # Part 1: When the man travels 400 km by train and the rest by car. # Part 2: When Ramesh travels 200 km by train and the rest by car. Part 1, Time taken by the man to travel 400km by train = 400/x hrs [∵ time = distance/ speed] Time taken by the man to travel (600 – 400) = 200 km by car = 200/y hrs Time taken by a man to cover 600 km = 400/x hrs + 200/y hrs Total time taken for this journey = 6 hours + 30 mins = 6 + 1/2 = 13/2 So, by equations its 400/x + 200/y = 13/2 400/x + 200/y = 13/2 400/x + 200/y = 13/2 200 (2/x + 1/y) = 13/2 2/x + 1/y = 13/400 .…(i) Part 2, Time taken by the man to travel 200 km by train = 200/x hrs. [∵ time = distance/ speed] Time taken by the man to travel (600 – 200) = 400 km by car = 200/y hrs For the part, the total time of the journey is given as 6 hours 30 mins + 30 mins that is 7 hrs, 200/x + 400/y = 7 200 (1/x + 2/y) = 7 1/x + 2/y = 7/200 …..(ii) Taking 1/x = u, and 1/y = v, So, the equations (i) and (ii) becomes, 2u + v = 13/400 ….. (iii) u + 2v = 7/200 ……. (iv) Solving (iii) and (iv), by (iv) x 2 – (iii) ⇒ 3v = 14/200 – 13/400 3v = 1/400 x (28 – 13) 3v = 15/400 v = 1/80 ⇒ y = 1/v = 80 Now, using v in (iii) we find u, 2u + (1/80) = 13/400 2u = 13/400 – 1/80 2u = 8/400 u = 1/100 ⇒ x = 1/u = 100 Hence, the speed of the train is 100 km/hr and the speed of the car is 80 km/hr.Read more on Sarthaks.com - https://www.sarthaks.com/633297/a-man-travels-600-km-partly-by-train-and-partly-by-car