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प्रश्न
The distance by road between two towns A and B is 216 km and by rail it is 208 km. A car travels at a speed of x km/hr and the train travels at a speed which is 16 km/hr faster than the car. Calculate:
- the time taken by the car to reach town B from A, in terms of x;
- the time taken by the train to reach town B from A, in terms of x.
- If the train takes 2 hours less than the car, to reach town B, obtain an equation in x and solve it.
- Hence, find the speed of the train.
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उत्तर
Speed of car = x km/hr
Speed of train = (x + 16) km/hr
i. We know: Time = `"Distance"/"Speed"`
Time taken by the car to reach town B From A = `216/x` hrs
ii. Time taken by the train to reach town B from A = `208/(x + 16)` hrs
iii. From the given information,
`216/x - 208/(x + 16) = 2`
`(216x + 3456 - 208x)/(x(x + 16)) = 2`
`(8x + 3456)/(x(x + 16)) = 2`
4x + 1728 = x2 + 16x
x2 + 12x – 1728 = 0
x2 + 48x – 36x – 1728 = 0
x(x + 48) – 36(x + 48) = 0
(x + 48)(x – 36) = 0
x = – 48, 36
But, speed cannot be negative.
So, x = 36.
iv. Speed of train = (36 + 16) km/hr = 52 km/hr.
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