Question

An express train makes a run of 240 km at a certain speed. Another train whose speed is 12 km/hr less than the first train takes an hour longer to make the same trip. Find the speed of express train in km/hr. explain its procedure also.

Answer 1

Let take ,
• properties of express train

distance covered by the express train = 240 km

speed of the express train = x km/h

time taken by the train = 240/x

( by using formula of "" speed = distance/time ; v = d/t : "")
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• properties of simple train

distance covered by the simple train = 240 km

speed of the simple train = x - 12 km/h

Time taken by the simple train = 240/x-12
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time taken by the simple train = time taken by the express train + 1 hour

240/x-12 = 240/x + 1

240/x-12 = 240+x/x

(cross multiplication)

240(x) = x-12(240+x)

240x = x(240+x)-12(240-x)

240x = 240x+x²-2880+12x

( cancel 240x from both side )

0 = x²+12x-2880

0 = x²+60x-48x-2880

0 = x(x+60)-48(x+60)

0 = (x+60)(x-48)

x = -60. OR. x = 48

( " speed value is always positive so " )
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• speed of a express train is = x = 48 km/h

• speed of a simple train is = x-12 = 48-12 = 36 km/h