Question

A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Answer 1

SOLUTION :  

Given: Total distance of a journey = 360 km

Let the original speed of the train  be x km/h  and the increased  speed of the train is (x + 5) km/h.

Time taken by the train with original speed to cover 360 km= 360/x hrs

[ Time = Distance/speed]

Time taken by the train with increased speed 360 km= 360/(x + 5) hrs  

A.T.Q

360 / x  -  360 /(x + 5) = 1

[360 (x + 5) - 360 x] /(x(x + 5) = 1

[By taking LCM]

360 x + 1800 - 360 x /(x² + 5x) = 1

1800 / x² + 5x = 1

x² + 5x  =  1800

[By cross multiplication ]

x² + 5x - 1800 = 0

x² - 40x + 45x - 1800 = 0

[By middle term splitting]

x(x - 40) + 45 ( x - 40) = 0

(x + 45) (x -  40) = 0

x = - 45 or  x = 40

Since, speed can't be negative, so x  ≠  - 45

Therefore,  x = 40 km/h  

Hence the original speed of the train 40 km/h .

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Answer 2

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