A boat carries passengers 10 miles upstream and then returns to the starting point. The total time of the boat trip is 2 hours. If the speed of the current is 3 miles per hour, what is the speed of the boat in still water?
speed of boat = v
upstream the speed relative to land is v-3
downstream it is v+3
total time: 10/(v-3)+10/(v+3)=2
multiply by (v+3)(v-3):
10(v+3)+10(v-3)=2(v+3)(v-3) = 2(v^2-3^3)
only positive solution is reasonable
v= 5+ sqrt(25+9)=5+sqrt(34) = 10.83 mi/hr
adding: 1.277+0.723=2 OK...
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