Question

A train covered a certain distance at a uniform speed. If the train had been 5 kmph faster, it would have been 3 hours less than the scheduled time. And, if the train was slower by 4 kmph, it would have taken 3 hours more than the scheduled time. Find the length of Journey. Please anyone give the step-by-step solution for the above question. Please. I want it immediately.

Answer 1

Speed= distance/ time
let the speed of the train be x and time taken y

Therefore if the train goes at 5km/hr faster;
its speed is (x+5)km/hr
and the time taken is (y+3)hours

On the other hand, if the train goes at 4km/hr slower;
its speed will be (x-4)km/hr 
and time taken will be (y-3)hours

After establishing these fats now you can form equations, using speed, time and distance formula:
speed=distance/time         and distance = time x speed
Since distance is the same for all the three instances, you can equate the equations for distance.

equation 1:

distance will be given by:   x times y = xy

equation 2: 

distance will be given by:  (x+5)(y-3)  = xy-3x+5y-15

equation 3:

distance will be given by: (x-4)(y+3) =xy+3x-4y-12
 
All these three equations are equal as they are equations for distance. Therefore equating any two equations will give you a linear equation you can use to solve for time, distance and speed.

hence xy = xy - 3x+5y - 15......therefore   3x - 5y = -15
                                                                   3x = 5y -15

and  xy = xy +3x - 4y-12   .......therefore  3x-4y =12
                                                   substitute for 3x >>>5y-15-4y =12
                                                                                      y=27

substitute for x:   3x=5y - 15
                           3x= 135-15    3x=120
                                                   x =40

therefore time taken = 27 hours
   while speed = 40km

distance= speed x time
             =27 x 40
             = 1080km
Therefore length of journey = 1080 kilometers

Answer 2

Answer:

1080 km

Step-by-step explanation:

Let the original speed of the train be x kmph and let the time taken to complete the journey be y hours.

Then, length of the journey = xy km.

Case I Speed = (x+5) kmph and time taken = (y-3) hours.

∴xy=(x+5)(y-3)⇒5y-3x=15... (i)

Case II Speed =(x-4)kmph and time taken =(y+3) hours

∴xy=(x-4)(y+3)⇒3x-4y=12... (ii)

From (i) and (ii), we get x=40andy=27 .

∴ length of the journey = xy=40×27 km = 1080 km.