Question

pratik takes 8 hours to travel 36 km downstream and return to the same spot.The speed of boat in still water is 12 km per hour.Find the speed of water current

Answer 1

36/12+c + 36/12-c =8
36(12-c +12+c)/144-c^2 =8
36×24/8 =144 -c^2
c^2 =144 - 108
c^2 = 36
c =6km/hr

Answer 2

Answer:

Speed of the current is 6 km/hr.

Step-by-step explanation:

Let the speed of the current be x km/hr.

Pratik goes 36 km downstream. 

Distance covered by the Pratik in Downstream = 36 km.

Speed of the Pratik in downstream = (12 + x) km/hr.

So, Time taken = 36/(12 + x)

Now, He also returned to the same spot.

Distance covered in upstream = 36 km.

Speed of the Pratik in upstream = (12 - x) km/hr. 

So, Time taken = 36/(12 - x)

Now,  

Time taken in upstream + Time taken in downstream = 8 hrs.

⇒36/(12 - x) + 36/(12 + x) = 8

⇒ 36(12 + x) + 36(12 - x) = 8(12 + x)(12 - x)

⇒ 36(12 + x + 12 - x) = 8(144 - 12x + 12x - x²)

⇒ 36(24) = 8(144 - x²)

⇒ 36 × 3 = 144 - x²

∴ x² = 144 - 108

∴ x² = √36

⇒ x = +6 or -6

-6 cannot be possible.

Hence Speed of the current is 6 km/hr.