Question

a train travel a distance of 480 km at a uniform speed had been 8 km/h less then it would be have taken 3 hours more to cover the same distance. we need to find the speed of the train in quadratic equation

Answer 1

let the speed of the train be x km/h.
Distance travelled by the train=480km
Therefore, time taken for travelling 480 km
=480/x h. because=time=distance/speed

if the speed had been 8km/h less, i. e. (x-8)km/h

then.
time taken for travelling 480km=480/x-8 h

according to the question.

480/x-8=3+480/x
=480/x-8-480/x=3
=480x-480(x-8)/x(x-8)=3
=480x-480x+3840=3x(x-8)
=3840=3x^2-24x
=3x^2-24x-3840=0
=3(x^2-8x-1280)=0
=x^2-8x-1280=0. (on dividing by 3 both sides)
=which is the required quadratic equation

Answer 2

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(i) Let us consider,

The breadth of the rectangular plot is x m.

Thus, the length of the plot = (2x + 1) m

As we know,

Area of rectangle = length × breadth = 528 m2

Putting the value of length and breadth of the plot in the formula, we get,

(2x + 1) × x = 528

⇒ 2x^2 + x = 528

⇒ 2x^2 + x – 528 = 0

Hence, 2x2 + x – 528 = 0, is the required equation which represents the given situation.

(ii) 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.....:)