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A motorboat takes 5 hours to travel 100 km going upstream.
The return trip takes 2 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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Your equations are
u - v = (1) (the speed moving upstream)
u + v = (2) (the speed moving downstream)
Or, which is the same
u - v = 20,
u + v = 50.
Add the two equations. You will get
2u = 20 + 50 = 70 ---> u = = 35 mph is the boat rate in still water.
Distract the first eq. from the second. You will get
2v = 50-20 = 30 ---> v = = 15 mph is the current rate.
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".