Question

Represent the following situation in the form of quadratic equations:-

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 3 hours more to cover the same distance.We need to find the speed of the train.​

Answer 1

Answer:

x²-8x- 1280

Step-by-step explanation:

Lets assume speed of train x km / hr

Lets assume time taken to travel t hrs.

Distance traveled = 480 km.

xt = 480 km      .................................. (i)

t = 480/x hr

reduced speed = (x-8) km / hr

new time taken to cover same distance =480 / (x-8)

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

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

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

480/(x-8)  - (480/x)  = 3

480(x−x+8)  / x(x-8) = 3

(480 * 8 ) / (x²-8x) = 3

480*8 = 3x²-24x

3x²-24x - (480*8) = 0

x²-8x- 1280 = 0

Reqd. quadratic equation =  x²-8x- 1280 = 0

​  

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.....:)