ram can row a boat 8km downstream and the same distance upstream in 1hr 40min if the speed of the stream is 2km/hr find the speed of the boat in still water
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speed of the stream = 2 km/hr
let speed of the boat in still water be x km/hr
Time taken to travel downstream = 8/(x+2)
Time taken to travel upstream = 8/(x-2)
Total time = 1 hr 40 min = 5/3 hr
8(x+2)+8(x−2)=538(x+2)+8(x−2)=53
24(x- 2) + 24(x+2) = 5(x+2)(x-2)
48x = 5x2 - 20
5x2 - 48x -20=0
x = 48±√(−48)2−4×5×(−20)2×548±(−48)2−4×5×(−20)2×5
=48±√2304+40010=48±2304+40010
=48±5210=48±5210
= 10 (taking only the positive value)
i.e., speed of the boat in still water = 10 km/hr
let speed of the boat in still water be x km/hr
Time taken to travel downstream = 8/(x+2)
Time taken to travel upstream = 8/(x-2)
Total time = 1 hr 40 min = 5/3 hr
8(x+2)+8(x−2)=538(x+2)+8(x−2)=53
24(x- 2) + 24(x+2) = 5(x+2)(x-2)
48x = 5x2 - 20
5x2 - 48x -20=0
x = 48±√(−48)2−4×5×(−20)2×548±(−48)2−4×5×(−20)2×5
=48±√2304+40010=48±2304+40010
=48±5210=48±5210
= 10 (taking only the positive value)
i.e., speed of the boat in still water = 10 km/hr
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