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A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours lessthan the scheduled time. And, if the train were slower by 6 km/hr ; it would have taken 6 hours more than the scheduled time. Find the length of the journey

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ago by (281k points)
 
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Solution:

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

Distance covered is xy km 

If the speed is increased by 6 km/hr, then time of journey is reduced by 4 hoursi.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) 

⇒−4x+6y−24=0 

⇒−2x+3y−12=0 …………………………….(i) 

Similarly xy=(x−6)(y+6) 

⇒6x−6y−36=0 

⇒x−y−6=0 ………………………………………(ii) 

Solving (i) and (ii) 

we get 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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