Question

A faster train takes 1 hour less than the slower train for the journey of 200km. If speed of faster train is 10km/h more, find the speed of two trains.​

Answer 1

Step-by-step explanation:

➸ Given :

• A faster train takes 1 hour less than the slower train for the journey of 200km. If speed of faster train is 10km/h more, find the speed of two trains.

➸ To Find :

• The speed of two trains.

➸ Solution :

Let the speed of the fast trainbe x km/h

Then, the speed of the slow train will be = (x -10) km/h

As we know,

$\bf\fbox{\blue{Speed = \frac{distance}{time}}}$

Time taken by the fast train to cover 200 km = 200/x hr.

And, time taken by the slow train to cover 200 km = 200/(x – 10) h

Since, the difference in the times is 1 hour.

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➤ According to the question,

$\implies \bf\frac{200}{x} - \frac{200}{x - 10} = 1$

$\implies \bf\frac{(200(x - 10) - 200x)}{x(x - 10)} = 1$

$\implies\frac{200x - 2000 - 200x}{ {x}^{2} - 10x } = 1$

$\implies$x² - 10x = -2000

$\implies$x2 – 10x + 2000 = 0

$\implies$x2 – 50x + 40x + 2000 = 0 [using factorisation method]

$\implies$x(x – 50) + 40(x – 50) = 0

$\implies$(x – 50)(x + 40) = 0 x = 50 or x = – 40

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As, the speed of train can never be negative we neglect x = -40

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Thus, speed of the fast train is 50 km/hr

And the speed of slow train (50 – 10) = 40 km/h

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➸ Final Result :

• Speed of the fast train = 50 km/hr
• Speed of the slow train = 40 km/hr