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-i

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