A boat carries passengers 10 miles upstream and then returns to the starting poi

label Algebra
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schedule 1 Day
account_balance_wallet $5

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?

May 4th, 2015

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

solution:

multiply by (v+3)(v-3):

10(v+3)+10(v-3)=2(v+3)(v-3) = 2(v^2-3^3)

20v=2v^2-18

2v^2-20v-18=0

v^2-10v-9=0

only positive solution is reasonable

v= 5+ sqrt(25+9)=5+sqrt(34) = 10.83 mi/hr

check:

10/(10.83-3)=1.277

10/(10.83+3)=0.723

adding: 1.277+0.723=2 OK...


May 4th, 2015

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