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
Answers
Answer:
Let speed of water current is x km/h
speed of boat in still water = 12 km/h
Distance = 36 km
Downstream speed = (12 + x) km/h
Upstream speed = (12 - x) km/h
A/C to question,
Total time taken by Pratik = 8 hrs
time taken to travel 36 km downstream + time taken to travel 36 km Upstream = 8hrs
⇒36/(12 + x) + 36/(12 - x) = 8
⇒ 36 [ 1/(12 + x ) + 1/(12 - x) ] = 8
⇒ 9[ {(12 - x) + (12 + x)}/(12² - x²) ] = 2
⇒9 × 24 = 2(144 - x²)
⇒ 9 × 12 = 144 - x²
⇒ 108 - 144 = - x²
⇒ x² = 36
⇒ x = ±6 , but speed ≠ negative
so, x = 6 km/h
Hence, speed of water current is 6 km/h
PLZ MARK AS BRIANLIEST AND THX FOR THE SUPERB QUESTION
Answer:
ok this is
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.
∴ Time taken =
(12+x)
36
Now, He also returned to the same spot.
∴ Distance covered in upstream =36 km.
Speed of the Pratik in upstream =(12−x) km/hr.
∴ Time taken =
(12−x)
36
Now,
Time taken in upstream + Time taken in downstream =8 hrs.
∴
(12−x)
36
+
(12+x)
36
=8
⇒36(12+x)+36(12−x)=8(12+x)(12−x)
⇒36(12+x+12−x)=8(144−12x+12x−x
2
)
⇒36×24=8(144−x
2
)
⇒36×3=144−x
2
∴x
2
=144−108
∴x=
36
⇒x=+6 or −6
−6 cannot be possible.
∴ Speed of the current is 6 km/hr.