Question

A train travels a distance of 480 km at a uniform speed if the speed had been 8 km per hour less then it would have taken 2 hours more to cover same distance we need to find speed of the train. the quadratic equation​

Answer 1

Answer:

40 km/hr

Step-by-step explanation:

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.

Answer 2

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Let us consider,

speed of train = x km/h

And

Time taken to travel 480 km = 480 (x) km/h

As per second situation, the speed of train = (x – 8) km/h

As given, the train will take 3 hours more 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

⇒ 3x^2 – 24x – 3840 = 0

⇒ x^2 – 8x – 1280 = 0

Hence, x^2 – 8x – 1280 = 0 is the required representation of the problem mathematically

Hope it's Helpful.....:)