A straight canal has motorboats departing from two terminals at...

Let the speed of the motorboats be $v$ and the departure interval be $T$.

The distance between two consecutive motorboats moving in the same direction is $vT$.

The speed of the tourist is $u = 20 \text{ km/h}$.

When the motorboats overtake the tourist, they are moving in the same direction. The relative speed is $v - u$. The time interval between consecutive overtakes is $18 \text{ minutes}$.

$(v - 20) \times \dfrac{18}{60} = v \times \dfrac{T}{60} \Rightarrow vT = 18(v - 20)$

When the motorboats cross the tourist in the opposite direction, the relative speed is $v + u$. The time interval between consecutive crossings is $6 \text{ minutes}$.

$(v + 20) \times \dfrac{6}{60} = v \times \dfrac{T}{60} \Rightarrow vT = 6(v + 20)$

Equating the two expressions for $vT$:

$18(v - 20) = 6(v + 20)$

$3(v - 20) = v + 20$

$3v - 60 = v + 20$

$2v = 80 \Rightarrow v = 40 \text{ km/h}$

Substituting $v = 40 \text{ km/h}$ into the second equation:

$40T = 6(40 + 20)$

$40T = 360 \Rightarrow T = 9 \text{ min}$

Answer: $40 \text{ km/h}, 9 \text{ min}$