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Question 1007654: A person rowed their boat downstream for 100 miles and they took 2 hours. Returning upstream, the trip took 2 hours and 40 minutes.
What is the speed of the water?
Found 3 solutions by mananth, ikleyn, n2:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!
Boat speed speed =x mph
stream speed =y mph
against stream 2 2/3 hours
with stream 2 hours
Distance with stream 100 miles distance against stream 100
t=d/r against stream (x-y)
100 / ( x - y )= 2 2/3
2 2/3 x - -2 2/3 y = 100 ....................1
with stream (x+y)
100 / ( x + y )= 2
2 ( x + y ) = 100
2 x + 2 y = 100 ...............2
Multiply (1) by 2
Multiply (2) by 2 2/3
we get 2
5 1/3 x + -5 1/3 y = 200
5 1/3 x + 5 1/3 y = 267
10 2/3 x = 467
/ 10 2/3
x = 43 3/4 mph
plug value of x in (1) y
2 2/3 x -2 2/3 y = 100
116 2/3 -2 2/3 -116 2/3 = 100
-2 2/3 y = 100
-2 2/3 y = -16 2/3 mph
y = 6 1/4
Boat speed 43 3/4 mph
stream 6 1/4 mph
CHECK
x+y= 50
X-y= 37 1/2
100 / ( 43 3/4 + 6 1/4 )= 2
100 / ( 43 3/4 )- 6 1/4 = 2 2/3
Answer by ikleyn(53742)  (Show Source):
You can put this solution on YOUR website! .
A person rowed their boat downstream for 100 miles and they took 2 hours.
Returning upstream, the trip took 2 hours and 40 minutes.
What is the speed of the water?
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In the post by @mananth, the solution is produced by a computer code.
Neither the style of the solution, nor its form of presentation are perfect;
they are difficult to read and to understand.
So, I present here my solution in simple, straightforward and clear, transparent form,
as it should be done to every school Math problem.
Let x be the rate of the boat in still water (in miles per hour)
and y be the rate of the current (in the same units).
Then the effective rate of the boat downstream is x + y
and the effective rate of the boat upstream is x - y.
From the problem, the effective rate of the boat downstream is the distance of 100 miles
divided by the time of 2 hours  = 50 mph.
The effective rate of the boat upstream is the distance of 100 miles
divided by the time of 2 hours and 40 minute, or 2 hours, or  hours
 =  = 37.5 mph
So, we have two equations for 'x' and 'y'
x + y = 50, (1)
x - y = 37.5. (2)
To find 'y', subtract equations (2) from equation (1). The terms 'x' and 'x' will cancel each other, and you will get
2y = 50 - 37.5 = 12.5 ---> y = 12.5/2 = 6.25.
At this point, the solution is complete.
ANSWER. The rate of the current is 6.25 miles per hour.
Solved.
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For a computer code (which @mananth uses to create his solution files),
there is no difference which style of the solution to produce.
But for a human reader, there is a huge difference what to read and from which source to learn.
So, I created my solution here in order for you see the difference.
Answer by n2(78)  (Show Source):
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