Question

an express train takes 30 mins less for a journey of 440km. its usual speed is increased by 8km/hr . find its usual speed​

Answer 1

${\bold{\boxed{\boxed{Answer = 80\:km/hr}}}}$

Given : The Train takes 30 mins less for a journey of 440km.

To Find : The usual speed of train.

Let the usual speed of the express train be x km/hr.

Then, the time taken by the express train to complete 440 km is

⇒ $Time\:taken$=$\frac{distace}{speed}$= $\frac{440}{x}hr$

Now, if the usual speed of the express train is increased by 8 km/hr, then the time taken to complete 440 km will be $\frac{distace}{speed}$= $\frac{440}{x+8}hr$

Now, By the given condition, we get:

$\frac{440}{x} - \frac{440}{x+8} = 30 \: min \: or \:\frac{1}{2}hr$

$⇒ 440 \times \frac{ x+ 8 - x}{[x(x + 8)]} = \frac{1}{2}$

$⇒ \frac{440 \times 8}{x^{2} + 8x} = \frac{1}{2}$

⇒x² + 8x = 7040

⇒x²+ 8x – 7040 = 0

On splitting the middle term 8x as 88x – 80x, we get:

⇒x² + 88x – 80x – 7040 = 0

⇒ x(x + 88) – 80(x + 88) = 0

⇒ (x + 88)(x – 80) = 0

⇒ x + 88 = 0 or x – 80 = 0

⇒ x = – 88 or x = 80

Since x is the usual speed of the express train, which cannot be negative, x = 80

Thus, the usual speed of the express train is 80 km/hr.