A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
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Answered by
6
speed = distance/time
time = distance/speed
Speed = x
time = 360/x
according to given
(x-5) (360/x - 1 ) = 360 (speed x time = distance) (speed = previous speed - 5km) ( time = previous time - 1hr less)
360x/x - x - 1800/x +5 =360
360 - x -1800/x + 5 = 360
360x + x^2 - 1800 + 5x = 360x
x^2 + 5x - 1800 = 0
x^2 + 45x - 40x -1800 = 0
(x + 45)(x - 40) = 0
x = -45, 40
time = 360 x 5 =
Answered by
1
Let us say, the speed of the train be x km/hr.
Time taken to cover 360 km = 360/x hr.
As per the question given,
⇒ (x + 5)(360-1/x) = 360
⇒ 360 – x + 1800-5/x = 360
⇒ x2 + 5x + 10x – 1800 = 0
⇒ x(x + 45) -40(x + 45) = 0
⇒ (x + 45)(x – 40) = 0
⇒ x = 40, -45
As we know, the value of speed cannot be negative.
Therefore, the speed of train is 40 km/h.
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