Convert speed in m/min to km /h
41 +2/3 m / min x 60 min = 2500 m/ hr = 2.5 km / hr
Let R be the rate of the boat in still water
[75% of 12 = 9]
And note that D /R = Total time
Rate downstream = R + 2.5 Rate upstream = R - 2.5
Distance downstream / Rate Downstream + Distance upstream/ Rate upstream = Total time
12 / [ R + 2.5] + 9 / [ R - 2.5 ] = 6
(12 [ R-2.5] + 9 [ R + 2.5] ) / [ (R+ 2.5 ) (R -2.5)] = 6
[ 12 R - 30 + 9R + 22.5]/ (R^2 - 6.25) = 6
21R - 7.5 = 6 [ R^2 - 6.25 ]
21R - 7.5 = 6R^2 - 37.5 rearrange as
6R^2 - 21R - 30 = 0 divide through by 3
2R^2 - 7R - 10 = 0
Using the quadratic formula
R = ( 7 + sqrt [ ( 7^2 - (4)*(2) *( -10)] ) / ( 2 * 2) = ( 7 + sqrt ( 129)) / 4 ≈ 4.6 km/h
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