Question

A passenger train covers a distance of 360 km at a certain speed. An express train 8 km/hr faster covers the distance in 1 hour 30 minutes less. Find the speed of the express train.

Answer 1

By sridharacharaya formula or discriminant method, we get 2 values of x then we neglect negative value

Answer 2

The speed of the express train is 48 km/hr

Solution:

Let the speed of passenger train = x

Then,

Speed of express train = x + 8

Total distance = 360 km

The formula is:

$time = \frac{distance}{speed}$

Then,

1 hour 30 minutes = 1.5 hour

So we get,

$\frac{360}{x} - \frac{360}{x + 8} =1.5\\\\360\left(x+8\right)-360x=1.5x\left(x+8\right)\\\\360x + 2880 - 360x = 1.5x^2 + 12x\\\\1.5x^2 + 12x - 2880 = 0\\\\15x^2+120x-28800=0$

$15\left(x^2+8x-1920\right) = 0\\\\\mathrm{Factor}\:x^2+8x-1920\\\\15\left(x-40\right)\left(x+48\right) = 0\\\\x = 40\\\\x = -48\\\\Ignore\ negative\ value\\\\Thus\\\\x = 40$

Find the speed of the express train

Speed of express train = x + 8

Speed of express train = 40 + 8 = 48

Thus the speed of the express train is 48 km/hr

Learn more:

A train covers the distance between two station which are 11km apart in 12min. At what rate per hours is it traveling?

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