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A motorboat takes 5 hours to travel 150mi going upstream. The return trip takes 3 hours going downstream.
What is the rate of the boat in still water and what is the rate of the current?
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Let x=rate of boat in still water
let c=rate of current
Then (x+c) is the rate of boat downstream
(x-c) is the rate of boat upstream
rate =
Rate upstream x-c = .
Rate downstream x+c = .
Simplify:
x - c = 30 (1)
x + c = 50 (2)
Add the equations (1) and (2). You will get
2x = 30 + 50 = 80 ====> x = = 40.
Answer. Rate of the boat in still water = 40 mph.
Rate of current = 10 mph.
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.