Question

a riverboat travels 72km downstrean in 3 hours. it travels 64 km upstream in 4 hours. find the speed of the boat and the speed of the stream

Answer 1

Below

Explanation:

rate x time = distance re-arrange to:

distance / time = rate

Rate downstream = 72/3 = 24

Rate upstream = 64/4 = 16

Difference/2 is the water speed (24-16) /2 = 4 mph

then boat speed = 16 + 4 = 20 mph

Answer 2

b = speed of the boat in still water

c = speed of the current

when going Upstream, the boat is not really going "b" fast, is really going slower, is going "b - c", because the current is subtracting speed from it, likewise, when going Downstream the boat is not going "b" fast, is really going faster, is going "b + c", because the current is adding its speed to it.

`{\Large \begin{array}{llll} \underset{distance}{d}=\underset{rate}{r} \stackrel{time}{t} \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lcccl} &\stackrel{Km}{distance}&\stackrel{kmh}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ Downstream&72&b+c&3\\ Upstream&64&b-c&4 \end{array}\hspace{5em} \begin{cases} 72=(b+c)(3)\\\\ 64=(b-c)(4) \end{cases} \\\\[-0.35em] ~\dotfill`

`72=(b+c)3\implies \cfrac{72}{3}=b+c\implies 24=b+c\implies 24-c=b \\\\[-0.35em] ~\dotfill\\\\ 64=(b-c)4\implies \cfrac{64}{4}=b-c\implies 16=b-c\implies \stackrel{\textit{substituting from above}}{16=(24-c)-c} \\\\\\ 16=24-2c\implies 16+2c=24\implies 2c=8\implies c=\cfrac{8}{2}\implies \boxed{c=4} \\\\\\ \stackrel{\textit{since we know that}}{24-c=b}\implies 24-4=b\implies \boxed{20=b}`