Answer:
<em>22 minutes</em>
Explanation:
<em>Let t be the time after 6 PM.
</em>
<em>
D be the distance </em>
<em>During time t, the First boat travelling south = 20t km.
</em>
<em>
Meanwhile, the second boat travelling east is= 15t km, </em>
<em>Then the second boat started 15 km from the dock, so the distance from the dock is= (15 - 15t) km. </em>
<em>The distance D between the two boats is is expressed as = (15 - 15t)^2 + (20t)^2 = D*2
</em>
<em>
Let differentiate with respect to time and making dD/dt to 0 (D minimization is important),
</em>
<em>
then 2(15 - 15t)(-15) + 2(20t)(20) = 0
</em>
<em>
Therefore t = 9/25 h or 0.36 h or 22 minutes</em>