. A train covered a certain distance at a uniform speed. If the train had been 6 kmph slower, it would have taken 12 hours more than the scheduled time. And, if the train were faster by 6 kmph, it would have taken 8 hours less than the scheduled time. Find the length of the journey.
Answers
Answer:
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