Inconsistent Downstream and Upstream Problem A boat takes $\frac{2}{3}$ as much time to travel downstream than to travel upstream. If the rate of the water is 8 kph, what is the rate of the boat in still water? Correct answer is 40kph Considering the following formulas: > v $\leftarrow$ speed of boat > > x $\leftarrow$ speed of river > > v-x is for upstream > > v+x is for downstream Also however, consider the wording: " A boat takes $\frac{2}{3}$ AS MUCH TIME to travel downstream". I am a bit confused here, does it pertain to ADDING time? as the boat goes downstream? downstream supposed to be faster so how can it add time? Does it pertain to multiplying $\frac{2}{3}$ to downstream or upstream? Any hint?

Since time is distance over speed, the time (in hours) it takes for the boat to travel $1$ km going upstream is: $$ \frac{1}{v + 8} $$ Likewise, the time needed to go downstream is: $$ \frac{1}{v - 8} $$ So we must solve the equation: $$ \frac{1}{v + 8} = \frac{2}{3} \cdot \frac{1}{v - 8} $$