A train travel 360 km at uniform speed.it the speed had been 5 kms/hr more,it would have taken 1 hour less for the same journey.find the speed of the train
Answers
Let the speed of the train = x km/h
increase speed of the train = (x+5)km/h
distance travelled by the train = 360km
time taken by the train = D/S=360/x hours
time taken by the train with increased speed = 360/x+5 hrs.
now according to condition
360/x - 360/x+5 = 1
360(x+5) - 360x = x(x+5)
360x + 1800 - 360x = xsquare + 5x
1800 = x^2 + 5x
x^2 + 5x - 1800 = 0
x^2 + 45x - 40x - 1800 =0
x(x+45) - 40(x+45) = 0
(x+45)(x-40) = 0
Now x+45= 0 or x-40 = 0
x = -45(Rejected) or x = 40
as speed cannot be 0 therefore, speed of the train = 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) = x^2 + 5x
⇒1800 = x^2 + 5x
⇒x^2 + 5x - 1800 = 0
⇒x^2 + 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
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