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A grain barge travels on a river from point A to point B loading and unloading grain. The barge travels at a rate of 8 mph
relative to the water. The river flows downstream at a rate of 1 mph. If the trip upstream takes 2 hours longer than the trip
downstream, how far is it from point A to point B?
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Let D be the distance between the points A and B.
The barge speed downstream is 9+1 = 10 mph relative to the bank of the river.
The barge speed upstream is 9-1 = 8 mph relative to the bank of the river.
Time moving downstream is hours.
Time moving upstream is hours.
The time difference equation is
= 2.
It is your equation to find D.
To solve it, multiply both sides by 40. You will get
5D - 4D = 80 ----> D = 80.
Answer. The distance under the question is 80 miles.
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
- 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".