Hyder Ali 600 km to his home partly by train and partly by car. He takes 8 hours if he travels 120 km by train and the rest by car. He takes 20 minutes longer if he travels 200 km by train and the rest by car. Find the speed of the train and the car.
- Speed of the train = 60 km/h, Speed of the car = 80 km/h.
- Speed of the train = 70 km/h, Speed of the car = 90 km/h.
- Speed of the train = 90 km/h, Speed of the car = 70 km/h.
- None of these
Explanation
Let the speed of the train be x km/h and the speed of the car be y km/h.
Case 1: He travels 120 km by train and the rest (480 km) by car, taking 8 hours in total.
Time taken by train = Distance / Speed = 120 km / x km/h = 120/x hours
Time taken by car = Distance / Speed = 480 km / y km/h = 480/y hours
Total time = 8 hours = (120/x) + (480/y)
Case 2: He travels 200 km by train and the rest (400 km) by car, taking 8 hours 20 minutes (or 8.33 hours) in total.
Time taken by train = Distance / Speed = 200 km / x km/h = 200/x hours
Time taken by car = Distance / Speed = 400 km / y km/h = 400/y hours
Total time = 8.33 hours = (200/x) + (400/y)
Now, we have two equations and two variables. Solving them simultaneously, we get:
x = 60 km/h (speed of the train)
y = 80 km/h (speed of the car)
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