a train travels 480km at a uniform speed. If the speed had been 10km/h more, it would have taken 4hours less for the same journey, find the speed of the train
Answers
Answer:
Let the speed of the train be x km/hr. Then
Time taken to travel a distance of 480km=
x
480
hr
Time taken by the train to travel a distance of 480km with the speed (x−8)km/hr=
x−8
480
hr
It is given that if the speed had been 8km/hr less, then the train would have taken 3 hours more to cover the same distance
∴
x−8
480
=
x
480
+3
⇒
x−8
480
−
x
480
=3⇒
x(x−8)
480(x−x+8)
=3⇒
x(x−8)
480×8
=3
⇒3x(x−8)=480×8⇒x(x−8)=160×8⇒x
2
−8x−1280=0
This is the required quadratic equation.
Step-by-step explanation:
Distance travelled by the train = 480 km
Let the speed of the train be x kmph
Time taken for the journey = 480/x
Given speed is decreased by 8 kmph
Hence the new speed of train = (x – 8) kmph
Time taken for the journey = 480/(x – 8)�
1280 = x2�– 8x
�x2�– 8x – 1280 = 0
On solving we get x = 40
Thus the speed of train is 40 kmph