Question

A train, which moves with uniform speed for a
certain distance takes 6 hours less if its speed is
increased by 6 km per hour, it would have taken 6
hours more, had its speed been decreased by 4 km
per hour. Find the distance of the journey and the
speed of the train.

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Answer 1

answer is 84km per hour

Step-by-step explanation:

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Answer 2

Answer:

distance of the journey and speed of the train is 720km

Step-by-step explanation:

Let the actual speed of the train be x km/hr and the actual time taken be y hours. Then,

Distance covered =(xy)km ..(i) [∴ Distance = Speed × Time]

If the speed is increased by 6 km/hr, then time of journey is reduced by 4 hours i.e., when speed is (x+6)km/hr, time of journey is (y−4) hours.

∴ Distance covered =(x+6)(y−4)

⇒xy=(x+6)(y−4) [Using (i)]

⇒−4x+6y−24=0

⇒−2x+3y−12=0 ..(ii)

When the speed is reduced by 6 km/hr, then the time of journey is increased by 6 hours i.e., when speed is (x−6) km/hr, time of journey is (y−6) hours.

∴ Distance covered =(x−6)(y+6)

⇒xy=(x−6)(y+6) [Using (i)]

⇒6x−6y−36=0

⇒x−y−6=0 (iii)

Thus, we obtain the following system of equations:

−2x+3y−12=0

x−y−6=0

By using cross-multiplication, we have,

3×−6−(−1)×−12x

= −2×−6−1×−12−y

= −2×−1−1×31

⇒

−30x

= 24−y

= −11

⇒x=30 and y=24

Putting the values of x and y in equation (i), we obtain

Distance =(30×24)km =720km.

Hence, the length of the journey is 720km.

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