Question

A boat takes twice as long to travel 5 km upstream as it does travel 3km downstream in a river that flows at a rate of 2 kph. At what speed does the boat travel in still water?

Answer 1

Answer: 22 kph

Step-by-step explanation:

distance (d) = rate (r) x time (t)

UPSTREAM: d = 5 km,   r = *x - y,  y = 2 kph,   t = 2t

DOWNSTREAM: d = 3 k,  r = *x + y,   y = 2 kph,   t = t

*x is the speed in still water and y is the current of the water.

Upstream equation:       5 = 2t(x - 2)   -->    $\dfrac{5}{2(x-2)}=t$

Downstream equation:  3 = t(x + 2)     -->    $\dfrac{3}{x+2}=t$

Set the equations equal to each other to solve for x:

$\dfrac{5}{2(x-2)}=\dfrac{3}{x+2}\\\\\\\text{Cross multiply:}\\5(x+2)=3\cdot2(x-2)\\\\\text{Distribute:}\\5x+10=6x-12\\\\\text{Isolate x:}\\10=x-12\\22=x$