## College Physics (4th Edition)

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.