Question

a train takes 2 hours less for a journey of 300 km of its speed is increased by 5 km per hour from its usual speed find the usual speed of the train

Answer 1

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$<i>$ Let, the usual speed of the train be x km/h

Now, time = distance / speed

So, the train will take time
= 300/x hours
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Speed of the train is increased by 5 km/h

So, speed of the train will be = (x+5)

So, the train will take time
= 300/(x+5) hours
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Now, as per the question, the train will take 2 hours less time,

So, by condition,
300/x - 300/(x+5) = 2
Or, [300(x+5) - 300(x)] / x(x+5) = 2
Or, 300x + 1500 - 300x = 2 * x(x+5)
Or, 1500/2 = x^2 + 5x
Or, x^2 + 5x = 750
Or, x^2 + 5x - 750 = 0
Or, x^2 + 30x - 25x - 750 = 0
Or, x(x+30) - 25(x+30) = 0
Or, (x-25)(x+30) = 0
Or, x = 25,(-30)

Since, speed can't be negative
So, (-30) is not acceptable.

Thus, usual speed of the train = 25 km/h
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➡️ Hence, the usual speed of the train is 25 km/h

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Answer 2

Answer:

Let the usual speed of the train be y km / hr .

A.T.Q.

$\displaystyle{\frac{300}{y} -\frac{300}{y+5} =2 }$

300 ( y + 5 ) - 300 y = 2 y ( y + 5 )

y² + 5 y - 750 = 0

y² + 30 y - 25 y - 750 = 0

( y + 30 ( y -25 ) = 0

y = - 30 or y = 25

Since , speed of train can't be negative .

Therefore , the usual speed of the train is 25 km / hr .