What is the rate of the water's current?

[Steph Annie]

Hello,

How should I go about setting this word problem up?
I am not looking for the answer, just some suggestion as to starting it.

I know it should be modeled as a rational expression.

"In still water, a boat averages 7 miles per hour. It takes the same amount of time to travel 20 miles downstream, with the current, as it does to travel 8 miles upstream, against the current. What is the rate of the water's current?"

 

[Deleted member 4993]

Hello,

How should I go about setting this word problem up?
I am not looking for the answer, just some suggestion as to starting it.

I know it should be modeled as a rational expression.

"In still water, a boat averages 7 miles per hour. It takes the same amount of time to travel 20 miles downstream, with the current, as it does to travel 8 miles upstream, against the current. What is the rate of the water's current?"

Define "stuff" to find and name those.

Here - What is the rate of the water's current - water speed = W

Let the speed of the boat in still water = B

Speed of boat - with the current = B + W

Speed of boat - against the current = B - W

Now use the equation Distance = speed * time ............. and continue....

 

[DrPhil]

Hello,

How should I go about setting this word problem up?
I am not looking for the answer, just some suggestion as to starting it.

I know it should be modeled as a rational expression.

"In still water, a boat averages 7 miles per hour. It takes the same amount of time to travel 20 miles downstream, with the current, as it does to travel 8 miles upstream, against the current. What is the rate of the water's current?"

First thing I do when translating a "word" problem from English to Algebra, is to look for the question. "What is the rate of the water's current?" Assign a variable name to the unknown:
......Let C = rate of current (mph)

Reading through a second time, I see the words "same time" for two different cases, so it may be a good idea to
......Let T = travel time (h)

The still-water speed ov the boat is 7 mph
......Speed with the current (downstream) = ...
......Speed against the current (upstream) = ...

The fundamental equation you need is distance = speed × time, or time = distance / speed
Set up the two equations for time, and make them equal.
Solve the resulting equation for C.