a boat first Travels 48 km downstream and 24 km upstream in 7 hours. then it travels for 9 hours ,going 48 km upstream and 36 km downstream .find the speed of the boat in still water and the speed of a of the current water.
Answers
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.⇔
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