Answer
Rowing rate in still water $=3$ miles per hour.
Rate of the current $=1.5$ miles per hour.
Work Step by Step
Let the average rowing rate in still water $=x$ miles per hour.
and the average rate of the current $=y$ miles per hour.
Effective speed with the current $=x+y$ miles per hour.
Effective speed against the current $=x−y$ miles per hour.
Use distance formual.
$\Rightarrow $Speed$×$Time$=$Distance
First condition (with the current):-
$9$ miles in $2$ hours.
Substitute all values into the formula.
$\Rightarrow (x+y)×2=9$
Multiply the equation by $3$.
$\Rightarrow (x+y)2\cdot 3=9\cdot 3$
Simplify.
$\Rightarrow (x+y)6=27$
Apply distributive property.
$\Rightarrow 6x+6y=27$......(1)
Second condition (against the current):-
$9$ miles in $6$ hours.
Substitute all values into the formula.
$\Rightarrow (x-y)×6=9$
Apply distributive property.
$\Rightarrow 6x-6y=9$......(2)
Add equation (1) and (2).
$\Rightarrow 6x+6y+6x-6y=27+9$
Add like terms.
$\Rightarrow 12x=36$
Divide both sides by $12$.
$\Rightarrow \frac{12x}{12}=\frac{36}{12}$
Simplify.
$\Rightarrow x=3$.
Substitute the value of $x$ into the equation (1).
$\Rightarrow 6(3)+6y=27$
Simplify.
$\Rightarrow 18+6y=27$
Subtract $18$ from both sides.
$\Rightarrow 18+6y-18=27-18$
Add like terms.
$\Rightarrow 6y=9$
Divide both sides by $6$.
$\Rightarrow \frac{6y}{6}=\frac{9}{6}$
Simplify.
$\Rightarrow y=\frac{3}{2}=1.5$
