SOLUTION: a motorboat can maintain a constant speed of 35 miles per hour relative to the water. the boat makes a trip upstream to a certain point in 30 minutes; the return trip takes 20 minu

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Question 1064441: a motorboat can maintain a constant speed of 35 miles per hour relative to the water. the boat makes a trip upstream to a certain point in 30 minutes; the return trip takes 20 minutes. what is the soeed of the current?
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website!
.
a motorboat can maintain a constant speed of 35 miles per hour relative to the water. the boat makes a trip upstream
to a certain point in 30 minutes; the return trip takes 20 minutes. what is the speed of the current?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let "v" be the speed of current, in miles per hour. Then the motorboat speed with the current is 35+v miles per hour. ( the speed relative to the bank of the river ) the motorboat speed against the current is 35-v miles per hour. (-------------------- " --------------------- ) The distance for the trip downstream is the same as upstream: = . (1) is of an hour = 30 minutes, is of an hour = 20 minutes. Multiply both sides of the eq.(1) by 6. You will get 3*(35-v) = 2*(35+v), 105 - 3v = 70 + 2v, 105 - 70 = 2v + 3v, 35 = 5v ----> v = = 7 mph. Answer. The current speed is 7 mph. The distance is = 14 miles. Check. Time upstream = = of an hour. Time downstream = = of an hour.

If you send me your comments/questions, please include the ID number of this problem (# 1064441) in order I could identify it.

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".

Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website!
mi/hr is the speed without a current
The 2 trips each have the same distance, in miles
Let = the speed of the current in mi/hr
-------------------------
Boat going upstream:
(1)
Boat going downstream:
(2)
( note that I converted minutes to hours )
---------------------------------------
(1)
(1)
(1)
and
(2)
(2)
(2)
-----------------------------
Add (1) and (2)
(1)
(2)
--------------------

--------------------
(1)
(1)
(1)
(1)
The speed of the current is 7 mi/hr
------------------
check:
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
OK