Question

With the current, you can canoe 72 miles in 4 hours. Against the same current, you can canoe only 3/4 of this distance in 6 hours. Find your rate in still water and the rate of the current.

Answer 1

Answer:

The rate in still water is 13.5 miles per hour and the rate of the current is 4.5 miles per hour.

Step-by-step explanation:

The velocity  of an object is equal to the displacement  divided by the time:

$v=\frac{d}{t}$

Going with the current the velocity in miles per hour is:

$v_1=\frac{72}{4}=18$

Going against the current, 3/4 of 72 miles is 54 miles, then the velocity in miles per hour is:

$v_2=\frac{54}{6}=9$

The velocity of going with the current is the sum of the rate of being still($s$) and the rate of the current($c$). And the velocity of going against is the difference between the two rates so:

$s+c=18$

$s-c=9$

Adding the equation to solve for $s$:

$\frac{{{s+c=18} \atop {s-c=9}}}{2s \ =27}$

$s=13.5$

Substituting $s$ in one equation to find $c$:

$s+c=18  \\ 13.5+c=18 \\ c=18-13.5 \\c=4.5$

The rate in still water is 13.5 miles per hour and the rate of the current is 4.5 miles per hour.