Solving of systems: Rowing speeds and current speeds?

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
tecnikal
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Solving of systems: Rowing speeds and current speeds?

Postby tecnikal » Sun Mar 01, 2009 7:57 pm

Rowing at 8km/h, in sitll water, Rima and Bhanu take 16 h to row 39 km down a river and 39 km back. Find the Speed of the current to two decimal places.

How would i set that up? my teacher taught my class to set up a kind of table but im not to sure how to. Any other methods out there?

Also>

A River flows at 2km/h, and John takes 6 h to row 16 km up the river and 16 km back. How fast did he row?

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stapel_eliz
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Postby stapel_eliz » Sun Mar 01, 2009 9:47 pm

tecnikal wrote:my teacher taught my class to set up a kind of table but im not to sure how to. Any other methods out there?

"Other methods" pretty much boil down to "keeping track of all the information in your head", etc. The tabular set-up is meant only to simplify "bookkeeping". :wink:

To review the "table" method for "uniform rate" exercises such as you've posted, try this online lesson. You'll see that the table's columns correspond to the "d", "r", and "t" in the "d = rt" equation you've learned. So, for instance, the first exercise you posted would be set up as:

+-------+----+-------+------------+
||||||||| d = r * t |
+-------+----+-------+------------+
| down | 39 | 8 + w | 39/(8 + w) |
+-------+----+-------+------------+
| up | 39 | 8 - w | 39/(8 - w) |
+-------+----+-------+------------+
| total | 78 ||||||||| 16 |
+-------+----+-------+------------+

The "w" stands for the speed of the water's current. The current pushes the boat (speeds it up) when they are going downstream, but retards the boat (slows it down) then they are coming back upstream. You'd fill in the "d" and "r" columns with the known information, and then solve "d = rt" for "t = d/r" to fill in the third column for "up" and "down". Then add the "up" and "down" times, and set equal to the "total" time.

Solve the rational equation for the value of "w". You should get two whole-number values; reject the negative answer (since the water doesn't run uphill!), and remember to put appropriate units (rate of speed) on your final answer.

Hope that helps! :D

Stranger_1973
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Re: Solving of systems: Rowing speeds and current speeds?

Postby Stranger_1973 » Wed Mar 11, 2009 3:20 pm

tecnikal wrote:A River flows at 2km/h, and John takes 6 h to row 16 km up the river and 16 km back. How fast did he row?

For this one, use "r=2" for the river current, so the equation is 16/(j-2) + 16/(j+2) = 6.


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