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A boat travels 30 miles up the river in the same amount of time it takes to travel 46 miles down the same river.
If the current is 4 miles per hour, what is the speed of the boat in still water?
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The governing equation is
= ("time" equation; u is the boat speed in still water)
Cross-multiply:
30*(u+4) = 46(u-4),
30u + 120 = 46u - 184,
120 + 184 = 46u - 30u,
304 = 16u ---> u = = 19.
Answer. The boat speed in still water is 19 mph.
It is a typical Upstream and Downstream round trips 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.
See especially the last of these three lessons, Problem 3.
It is exactly your sample/prototype.
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".