SOLUTION: The current in a stream moves at a speed of 7 mph. A boat travels 38 mi upstream and 38 mi downstream in a total time of 3 hr. What is the speed of the boat in still​ water?

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Question 1057506: The current in a stream moves at a speed of 7 mph. A boat travels 38 mi upstream and 38 mi downstream in a total time of 3 hr. What is the speed of the boat in still​ water?
And,
The outside of a picture frame measures 14 in by 20 in. 184 in. squared of the picture shows. Find the thickness of the frame.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!
                SPEED       TIME      DISTANCE
UPSTREAM        r-7         38/(r-7)    38
DOWNSTR         r+7         38/(r+7)    38
Total                         3



Uniform width of frame, ok, but not enough information for its thickness.
Width of frame instead:
;
which is, the given picture area is equal to the inner frame area.
Answer by ikleyn(52834)   (Show Source): You can put this solution on YOUR website!
.
The current in a stream moves at a speed of 7 mph. A boat travels 38 mi upstream and 38 mi downstream in a total time of 3 hr.
What is the speed of the boat in still water?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let "u" be the speed of the boat in still water.
Then the boat speed moving downstream is (u+7) mph,
while the speed moving upstream is (u-7).

The time traveling upstream is    hours.
The time traveling downstream is    hours.

The total time for the round trip is   +  hours.

And the equation is 

 +  = 3.    ("time" equation).

To solve it, multiply both sides by (u-7)*(u+7).

You will get

38*(u+7) + 38*(u-7) = .

Simplify:

 = ,

 = 0.

Solve using the quadratic formula

 =  = .

We are interested in positive root only.

It is u =  =~ 13.569 km/h (approximately).

Check.   +  = 3.000 hours.

Answer.  The boat speed in still water is 13.569 km/h (approximately).

Solved.

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 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".


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