A train travels 360 km at a uniform speed. if the speed of the train had been 5 km/h more, it would have taken one hour less for the same journey. Find the original speed of the train.
Answers
Answer:
Explanation:
Solution :-
Let the Original speed of train be x km/h.
Time taken to cover 360 km = 360/x h
Time taken to cover km with the speed of (x + 5) km/h = 360/x + 5
According to the Question,
⇒ 360/x - 360/x + 5 = 1
⇒ 360(x + 5) - 360x/x(x + 5) = 1
⇒ 360x + 1800 - 360x/x(x + 5) = 1
⇒ x² + 5x - 1800 = 0
⇒ x² + 45x - 40x - 1800 = 0
⇒ x(x + 45) - 40(x + 45) = 0
⇒ (x + 45) (x - 40) = 0
⇒ x = - 45, 40 (Neglecting negative sign)
⇒ x = 40 km/h
Hence, the original speed of the train is 40 km/h.
Answer:
Let the original speed of the train be x km/h.
Time taken to cover a distance of 360 km = 360/x hours.
New speed of the train = (x+5) km/h.
Time taken to cover a distance of 360 km at new speed = 360/x+5 hours.
Since, the train takes 1 hour less time,
∴ 360/x - 360/ x+5 = 1
⇒360 (x+5-x)/x(x+5) = 1
⇒360 (5) = x² + 5x
⇒1800 = x² + 5x
⇒x² + 5x - 1800 = 0
⇒x² + 45x - 40x - 1800 = 0
⇒x (x+45) - 40( x +45) = 0
⇒(x+45) (x-40) = 0
⇒x = (-45), 40
But since speed cannot be in negative.
∴ x = 40 km/hr.
Hence, the original speed of the train is 40 km/h.
hope it helps u