A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.
Answers
Answer:
10th
Maths
Quadratic Equations
Standard Form of Quadratic Equations
A train travels a distance ...
MATHS
A train travels a distance of 480km at a uniform speed. If the speed had been 8km/hr less, then it would have taken 3 hours more to cover the same distance. Formulate the quadratic equation in terms of the speed of the train.
MEDIUM
Share
Study later
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.
Let us consider,
The speed of train = x km/h
And
Time taken to travel 480 km = 480/x km/hr
As per second condition, the speed of train = (x – 8) km/h
Also given, the train will take 3 hours to cover the same distance.
Therefore, time taken to travel 480 km = 480/(x+3) km/h
As we know,
Speed × Time = Distance
Therefore,
(x – 8)(480/(x + 3) = 480
⇒ 480 + 3x – 3840/x – 24 = 480
⇒ 3x – 3840/x = 24
⇒ 3x2 – 8x – 1280 = 0
Therefore, the speed of the train, satisfies the quadratic equation, 3x2 – 8x – 1280 = 0, which is the required representation of the problem mathematically.