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The current of a river is 4 miles per hour. A boat travels to a point 48 miles upstream and back in 5 hours. What is the speed of the boat in still water?
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Your equation is
= 5.
Here u is the unknown speed of the boat in still water.
The first addend in the left side is the time spent by the boat traveling upstream.
The second term is the time spent traveling downstream.
To solve equation (*), multiply both sides by (u-4)*(u+4). You will get
48(u+4) + 48(u-4) = 5(u^2-16), or
5u^2 - 96u - 80 = 0.
Solve using quadratic formula:
= = .
Disregard the negative root.
The solution is u = 20.
Answer. The boat speed in still water is 20 mph.
It is a typical Upstream and Downstream round trips word problem.
You can find similar fully solved similar problems on upstream and downstream round trips with detailed solutions in the 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
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".