Question

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. We need to
find the speed of the train.​

Answer 1

Given :

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

To find :

We need to  find the speed of the train.​

Solution:

Let the speed of train be x

Distance traveled by train = 480 km

$Time = \frac{Distance}{Speed}\\Time = \frac{480}{x}$

The speed had been 8 km/h  less

New speed = x-8

So, $Time = \frac{Distance}{Speed}\\Time = \frac{480}{x-8}$

We are given that  If the speed had been 8 km/h  less, then it would have taken 3 hours more to cover the same distance.

So,$\frac{480}{x-8}-\frac{480}{x}=3\\\frac{480x-480x+3840}{(x-8)(x)}=3\\\frac{3840}{x^2-8x}\\\frac{1280}{x^2-8x}=1\\1280=x^2-8x\\x^2-8x-1280=0\\(x-40)(x+32)=0\\x=40,-32$

So, Speed of the train is 40 km/hr

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.....:)