7. 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
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.
Have a Marvelous Day. :)