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

please give the detailed answer friends​

Answer 1

$\bf\huge\underline{Question}$⠀

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

$\bf\huge\underline{Solution}$⠀

Let the speed of the train = u km/hr

Distance covered = 480 km

Time taken = $\dfrac{Distance}{Speed}$ = $\dfrac{480}{u}$

In second case,

speed = (u - 8) km/hour

Therefore, time taken = $\dfrac{Distance}{speed}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\dfrac{480}{(u - 8)}$

According to the condition,

⠀⠀$\dfrac{480}{u - 8}$ - $\dfrac{480}{u}$ = 3

=> 480u - 480(u - 8) = 3u(u - 8)

=> 480u - 480u + 3840 = 3u² - 24u

=> 3840 - 3u² + 24u = 0

=> u² - 8u - 1280 = 0

⠀

Thus, the required quadratic equation is u² - 8u - 1280 = 0

Answer 2

${\huge{\sf{\bold{\boxed{\color{Pink}{Answer}}}}}}$

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.....:)