SOLUTION: The current of a river is 2 2 miles per hour. A boat travels to a point 24 24 miles upstream and back in 5 5 hours. What is the speed of the boat in still water?

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Question 1064973: The current of a river is
2
2 miles per hour. A boat travels to a point
24
24 miles upstream and back in
5
5 hours. What is the speed of the boat in still water?
Found 3 solutions by Boreal, josgarithmetic, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x= speed of boat
(x-2) is speed upstream and 24/(x-2) is hours it takes to go 24 miles.
(x+2) is speed downstream, and 24/(x+2) is hours it takes to go 24 miles.
Those two times add to 5 hours
Multiply by (x-2)(x+2) or x^2-4 as common denominator,
24(x+2)+24(x-2)=5x^2-20
0=5x^2-48x-20
(5x+2)(x-10)=0
x=10 mph in still water.
so 8 mph upstream and takes 3 hours to go 24 miles
and 12 mph downstream and takes 2 hours to go 24 miles. Total time 5 hours.

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
r, speed in still water 
                   SPEED     TIME          DISTANCE
UPSTREAM             r-2     24/(r-2)          24

Back DOWNSTREAM      r+2     24/(r+2)         24

Total                         5


24%2F%28r-2%29%2B24%2F%28r%2B2%29=5
Solve this for r.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
The equation by "josgarithmetic" is WRONG.


The correct equation is

24%2F%28r-2%29+%2B+24%2F%28r%2B2%29 = 5.

r-2 is the speed of the boat upstream.

r+2 is the speed of the boat downstream.


It is a typical and standard Upstream and Downstream round trip word problem.
You can find many similar fully solved problems on upstream and downstream round trips with detailed solutions in lessons
    - Wind and Current problems
    - More problems on upstream and downstream round trips
    - Selected problems from the archive on the boat floating Upstream and Downstream
in this site.

Read them attentively and learn how to solve this type of problems once and for all.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the section "Word problems", the topic "Travel and Distance problems".