Answer
The boat is 187 meters away.
Work Step by Step
We can use the speed $v_1$ and the travel time $t_1$ of the 1.0-Hz waves to write an expression for the distance:
$d = v_1~t_1$
Note that $t_2 = t_1+120~s$. We can use the speed $v_2$ and the travel time $t_2$ of the 2.0-Hz waves to write an expression for the distance:
$d = v_2~t_2 = v_2~(t_1+120~s)$
Since the distance is the same, we can equate the two equations to find $t_1$:
$v_1~t_1 = v_2~(t_1+120~s)$
$(v_1-v_2)~t_1 = (120~s)~v_2$
$t_1 = \frac{(120~s)~v_2}{v_1-v_2}$
$t_1 = \frac{(120~s)(0.78~m/s)}{1.56~m/s-0.78~m/s}$
$t_1 = 120~s$
We can find the distance $d$:
$d = v_1~t_1 = (1.56~m/s)(120~s) = 187~m$
The boat is 187 meters away.
