1. ## Word probelm help!!!

I have a review due tomorrow and these word problems are killing me!!! I would greatly appreciate it if anyone could help, here they are

1. The force of a wind varies jointly with the window surface area and the square of the velocity of the wind. If the force is 40 pounds on a surface area of 12 square feet when the wind is 10 mph, what is the force on a surface area of 20 square feet when the wind is 30 mph?

2. How many liters of water must be added to 20 liters of a 5% salt solution to dilute it to a 1% salt solution?

3. A boat can travel 20 mph in still water. It can travel 75 miles downstream in the same time that it requires to travel 45 miles upstream. Find the rate of the stream.

2. Originally Posted by Help!
I have a review due tomorrow and these word problems are killing me!!! I would greatly appreciate it if anyone could help, here they are

1. The force of a wind varies jointly with the window surface area and the square of the velocity of the wind. If the force is 40 pounds on a surface area of 12 square feet when the wind is 10 mph, what is the force on a surface area of 20 square feet when the wind is 30 mph?

2. How many liters of water must be added to 20 liters of a 5% salt solution to dilute it to a 1% salt solution?

3. A boat can travel 20 mph in still water. It can travel 75 miles downstream in the same time that it requires to travel 45 miles upstream. Find the rate of the stream.
1. Let the window surface be A $\displaystyle (ft)^2$ and the wind speed be v $\displaystyle mph$

$\displaystyle F \propto Av^2$

$\displaystyle 40 = k \times 12 \times 10^2$

$\displaystyle k = \frac{40}{1200} = \frac{1}{30}$

$\displaystyle F_2 = kAv_2^2 = \frac{1}{30} (20)(30^2) = 600$ Apparently your units should be pounds but that's not a unit of force...

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2. Assuming you mean percentage by volume:

A 5% solution in 20L means that there is 20*0.05L = 1L of salt. To make this a 1% solution you need to keep the 1 = 0.01*V. V = 100 and so you need to add 100-20 (for you have 20 already) = 80L

(you may want to get this checked)

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3.Let the current be v mph.

Going downriver you have $\displaystyle \frac{75}{20+v}$

Going upriver you have $\displaystyle \frac{45}{20-v}$

Equate these to find v: $\displaystyle \frac{75}{20+v} = \frac{45}{20-v}$

$\displaystyle 75(20-v) = 45(20+v)$

$\displaystyle 1500 - 75v = 900+45v$

$\displaystyle 600 = 120v$

$\displaystyle v = 5mph$

3. thank you very much!!!