Question

Represent the given situation in the forms of quadratic equation. a train travels a distance of 480 km at a uniform speed if the speed had been 8 km per hour less than it would have taken 3 hours more to cover the same distance we need to find the speed of the train​

Answer 1

Answer:

40km/hr

Step-by-step explanation:

distance =480km

let the speed be x

and time be t

speed = distance /time

x=480/t

same as ,t=480/x ......................(1)

also,

x-8=480/(t+3).......................(2)

substitute t with (1) in (2)

x-8=480/(480/x+3)

(x-8)(480/x+3)=480

480 +3x -3840/x -24=480

3x -3840/x -24=0

3x^2-3840-24x=0

x^2-8x-1280=0

x^2-40x+32x-1280=0

x(x-40)+32(x-40)=0

(x-40)(x+32)=0

x=40 or x= -32

x can't be negative so x =40km/hr

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.....:)