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
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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
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Verified answer
Let speed of water current is x km/hspeed 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
Verified answer
Hello Dear.Good Question , Your answer is here.
Let the Speed of the Water Current be x km/hr.
→In Case of the Downstream,←
Distance Covered by the Boat in Downstream = 36 km.
Speed of the Boat in Downstream = (12 + x) km/hr.
Using the Formula,
→ Speed = Distance/Time
→ Time(T1) = 36/(12 = x) hrs.
→In case of Upstream,←
Distance covered by the Boat in Upstream = 36 km.
Speed of the Boat in Upstream = ( 12 - x) km/hr.
Thus, Time(T2) = 36/(12 - x) hrs.
⇒According to the Question,
T1 + T2 = 8 hrs.
36/(12 + x) + 36/(12 - x) = 8
36[ 12 - x + 12 + x] = 8(12 - x)(12 + x)
36 × 24 = 8 [144 - x²]
⇒ 108 = 144 - x²
x² = 144 - 108
x² = 36
x = √36
x = +6 or x = -6
Since x = -6 cannot be possible because speed of the current cannot be negative.
⇔Thus, Speed of the Water Current is 6 km/hr.⇔
I anticipate it will help u.
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