Question

a train covers a distance of 300 km at the universe speed . Speed of train is increased by 5 km per hour is takes 2 hours in the journey find original speed of the train?

Answer 1

Hello!!!
Your answer is here ...

Let the speed of train be = x
Total distance travelled = 300 km

Time= distance/speed
=>300/x -------(1.)

according to the question Speed of train is increased by 5 km per hour so,
New speed = x+5

Time = distance / new speed
=>300/x+5 -------(2.)

Time taken to complete= 2 hours

Therefore
From eq.(1.) nd eq.(2.)
$\frac{300}{x} - \frac{300}{x + 5} = 2 \\ \\ \frac{300(x + 5) - 300x}{x(x + 5)} = 2 \\ \\ \frac{300x + 1500 - 300x}{ {x}^{2} + 5x } = 2 \\ \\ 1500 = 2( {x}^{2} + 5x) \\ \\ 1500 = 2 {x}^{2} + 10x \\ \\ {2x}^{2} + 10x - 1500 = 0 \\ \\ 2 {x}^{2} + 60x - 50x - 1500 = 0 \\ \\ 2x(x + 30) - 50(x + 30) = 0 \\ \\ \\ (2x - 50)(x + 30) = 0$

Now,

2x-50=0
2x=50
x=50/2
x=25 km/hr

x+30=0
x=-30 km/hr

Now, speed can't be in negative .

So, the original speed of the train is $\bold{\underline{25 \:km/hr}}$