Question 1180103: Traveling downstream,a boat traveled a 48 km long river in 40 min.The boat took an hour to travel back upstream.what is the rate of the boat in still water?what is the rate of the current?State you answers in km/h.Show your solution
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source):
Answer by ikleyn(52803)  (Show Source):
You can put this solution on YOUR website! .
Traveling downstream, a boat traveled a 48 km long river in 40 min.
The boat took an hour to travel back upstream.
what is the rate of the boat in still water?
what is the rate of the current?
State you answers in km/h. Show your solution
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First ignore the post by @josgarithmetic.
It is his usual gibberish, which will lead you to NOWHERE.
The boat rate downstream is 48 km in 40 minutes.
Since 40 minutes = 2/3 of an hour, this rate is  = 72 kilometers per hour.
The boat's rate upstream is 48 kilometers per hour.
The rate downstream is the sum of the rate of the boat in still water "u" and the rate of the current "v".
So, you have your first equation
u + v = 72 (1)
The rate upstream is the DIFFERENCE of the rate of the boat in still water "u" and the rate of the current "v".
So, you have your second equation
u - v = 48. (2)
Now you need to solve this system of equations. For it, add equations (1) and (2). You will get then
2u = 72 + 48 = 120
u = 120/2 = 60.
To find v, substitute the found value u = 60 into equation (1). You will get
60 + v = 72,
v = 72 - 60 = 12.
The problem is just solved, and the ANSWER is
+------------------------------------------------------+
| the rate of the boat in still water is 60 km/h |
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| the rate of the current is 12 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, 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.
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Do not forget to post your "THANKS" to me for my teaching.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Traveling downstream,a boat traveled a 48 km long river in 40 min.The boat took an hour to travel back upstream.what is the rate of the boat in still water?what is the rate of the current?State you answers in km/h.Show your solution-
I agree. The other person's setup is PURE RUBBISH!!
Let the speeds of the boat in calm water, and current, be S and C, respectively
Then we get the following AVERAGE-SPEED equations:
2S = 120 ------ Adding eqs (i) and (ii)
Speed of boat, in still water, or 
Now, substitute 60 for S in eq (i) and solve for C to get speed of the current.
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