Question

a motorboat travels 305km in 5 hours going upstream and 651km in 7 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

Recall your d = rt, distance = rate * time.

b = speed rate of the boat.

c = speed rate of the current.


keeping in mind that, as the boat goes Upstream, against the current, it's speed is not "b", but is really " b - c ", because the current is subtracting speed from it.

likewise, when the boat is going Downstream, because is going with the current, is really going faster at " b + c ".

$\bf \begin{array}{lccclll} &\stackrel{km}{distance}&\stackrel{kmh}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ Upstream&305&b-c&5\\ Downstream&651&b+c&7 \end{array} \\\\\\ \begin{cases} 305=(b-c)(5)\implies 61=b-c\implies 61+c=\boxed{b}\\ 651=(b+c)(7)\implies 93=b+c\\ ----------------------\\ 93=\boxed{61+c}+c \end{cases} \\\\\\ 93=61+2c\implies 32=2c\implies \cfrac{32}{2}=c\implies 16=c$

what is the speed of the boat?  well, 61 + c = b.