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A boat traveled 465 miles downstream and back. The trip downstream took 12 hours. The trip back took 31 hours.
Find the speed of the boat in still water and the speed of the current?
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Let u be the speed of the boat in still water (in mph),
v be the speed of the current.
Then these two equations are in the place
u + v = , (1)
u - v = . (2)
To solve the system, add the two equations. You will get
2u = + , hence, u = mph.
Then distract the two equations. You will get
2v = - , hence, v = mph.
EXPANATIONS:
If u is the speed of the boat in still water and v be the speed of the current, then the speed of the boat traveling downstream
is (u+v) relative to the bank of the river.
The speed of the boat traveling upstream is (u-v) relative to the bank of the river.
From the other side, in the right side of the equation (1) is the speed of the boat traveling downstream.
in the right side of the equation (2) is the speed of the boat traveling upstream.
So, the equations (1) and (2) are direct and literal translation of the condition to the math language.
The rest, i.e. the solution of the system itself, was explained above.
It is a typical and standard Upstream and Downstream round trip word problem.
You can find 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".