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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.
.
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?
~~~~~~~~~~~~~~~~~~~
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.