SOLUTION: A boat takes 2/3 as much time to travel downstream as to its return. If the rate of the river's current is 8 kph, what is the rate of the boat i still water?

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Question 1105953: A boat takes 2/3 as much time to travel downstream as to its return. If the rate of the river's current is 8 kph, what is the rate of the boat i still water?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
A boat takes 2/3 as much time to travel downstream as to its return. If the rate of the river's current is 8 kph,
what is the rate of the boat highlight%28cross%28i%29%29 in still water?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let  "x"  be the the rate of the boat in still water.


Then its effective rate downstream is (x+8) km/h,

while the effective rate upstream is (x-8) km/h.


The "time equation" is 


D%2F%28x%2B8%29 = %282%2F3%29%2A%28D%2F%28x-8%29%29,       (<<<---=== it says "time downstream = 2/3 time upstream")


where D is one way distance.


You can cancel the factor D.  After that, multiply both sides by  3*(x-8)*(x+8)  to get

3*(x-8) = 2*(x+8),

3x - 24 = 2x + 16,

3x - 2x = 16 + 24  ====>  x = 40.


Answer.  the rate of the boat in still water is 40 km/h.

Solved.


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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.

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 greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The response from the other tutor is a perfectly good one....

I set up the problem a bit differently than she does and arrive at the same equation by a different path.

Take a look at both methods and see if one of them "works" better for you.

Since the ratio of times for the downstream and upstream trips is 2:3, the ratio of speeds must be 3:2.
Then, since the upstream and downstream distances are the same, 3 times the upstream rate must equal 2 times the downstream rate.
And since the rate of the current is 8 kph, the upstream and downstream speeds are x-8 and x+8. So

3%28x-8%29+=+2%28x%2B8%29

which is the same equation she ended up with by a different path. And so of course the solution from there is as she shows it.