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

label Algebra
account_circle Unassigned
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

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
May 4th, 2015
...
May 4th, 2015
Oct 19th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer