Question

train travels a distance of 300 km at constant speed. If the speed of the train is increased by 5 km an hour the journey would have to take 2 hours less, we need to find the original speed of the train

Answer 1

Answer:

25kmph

Step-by-step explanation:

In the image above..

I didn't solve it very deeply but still hope it helps....

Answer 2

Answer:

$\boxed{\sf The \;original \;speed \;of\; the\; train \; is \;25km/hr.}$

Step-by-step explanation:

$\bigstar$ Let the original speed of the train be x km/hr.

∴ The time taken to cover 300km = $\dfrac{300}{x} hr$

∴ The time taken to cover the same 300km , if the speed is increased by 5km/hr will be ,

$\bigstar$  $\dfrac{300}{x+5} hrs$

∵ It is given that the if speed is increased by 5 km/hr, the journey would have to take 2 hours less.

$\dfrac{300}{x} - \dfrac{300}{x+5} = 2$

On crossing the terms,

$\implies$ $\dfrac{300(x+5)-300x}{x(x+5)} = 2$

On Simplification,

$\implies$

$\dfrac{300x + 1500 - 300x }{x\²+5x}=2$

$\dfrac{1500}{x\²+5x} = 2$

1500 = 2(x²+5x)

1500 = 2x²+10x

2x²+10x-1500 = 0

On dividing the whole equation by 2

x²+5x-750 = 0

Middle term splitting to find the roots

Product = -750 and Sum = 5

The Numbers satisfying these conditions are:-

30 and -25

∴ x²+30x−25x−750=0

∴ (x+30)(x−25)=0

So,

x = -30 or x = 25

But here x is speed so x must be positive .

∴ x = 25km/hr.