SOLUTION: A boat on a river travels downstream between two points, 20 miles apart, in one hour. The return trip against the current takes 2 1/2 hours. What is the speed, and how fast does th

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Question 1146980: A boat on a river travels downstream between two points, 20 miles apart, in one hour. The return trip against the current takes 2 1/2 hours. What is the speed, and how fast does the current in the river flow?
Found 2 solutions by ikleyn, richwmiller:
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.
Let u = speed of the boat in still water (miles per hours), and

    v = speed of the current.


Then you have these two equation 


    u + v =       (1)   effective rate of the boat traveling downstream

    u - v =    (2)  effective rate of the boat traveling upstream  (notice   =  hours)


Equivalently


    u + v = 20    (3)

    u - v = 8     (4)


Add the equations (3) and (4) to get


    2u = 20 + 8 = 28,  ====>  u = 28/2 = 14 mph  is the boat speed in still water


Then from equation (3)    v = 20 - 14 = 6 mph is the speed of the current.

Solved.

-------------------

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
    - Wind and Current problems solvable by quadratic equations
    - Unpowered raft floating downstream along a river
    - Selected problems from the archive on the boat floating Upstream and Downstream
in this site, where you will find other similar solved problems with detailed explanations.

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".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Take advantage of tutor ikleyn's 886 lessons that she graciously provided for free.
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