A boat travels 30km upstream and 44km downstream in 10 hours. in 13 hours it can travel 40km upstream and 55km downstream. Determine the speed of the stream and that of the boat in still water. (in km/hr)


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Question Number 56503 by otchereabdullai@gmail.com last updated on 17/Mar/19

$A boat travels 30 km upstream and$ $44 km downstream in 10 hours .$ $in 13 hours it can travel 40 km upstream$ $and 55 km downstream . Determine the$ $speed of the stream and that of the$ $boat in still water . (in km / hr)$
	Answered by MJS last updated on 17/Mar/19

	$\frac{30}{(v_{b} - v_{s})} + \frac{44}{(v_{b} + v_{s})} = 10$ $\Rightarrow 5 v_{b}^{2} - 5 v_{s}^{2} - 37 v_{b} + 7 v_{s} = 0 (1)$ $\frac{40}{(v_{b} - v_{s})} + \frac{55}{(v_{b} + v_{s})} = 13$ $\Rightarrow 13 v_{b}^{2} - 13 v_{s}^{2} - 95 v_{b} + 15 v_{s} = 0 (2)$ $- \frac{13}{5} (1) + (2)$ $\frac{6}{5} v_{b} - \frac{16}{5} v_{s} = 0 \Rightarrow v_{s} = \frac{3}{8} v_{b}$ $insert in (1)$ $\frac{275}{64} v_{b}^{2} - \frac{275}{8} v_{b} = 0$ $v_{b} > 0 \Rightarrow v_{b} = 8 k m / h r \Rightarrow v_{s} = 3 k m / h r$
	Commented by otchereabdullai@gmail.com last updated on 18/Mar/19

	$thanks prof$
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