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Here's the question I'm having trouble with. Ken and Kara are 30 miles apart on a calm lake paddling towards each other. Ken paddles at 4 mph, while Kara paddles at 7 mph. HOw long will it take them to meet?

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How much closer to each other are they after one hour? –  Henning Makholm Feb 1 '12 at 17:56
    
@HenningMakholm Ken is 4miles closer and kara is 7 miles closer. Therefor the gap between them is now 19 miles. After 2 hrs the gap would be 8miles. Got it: 4x + 7x = 30 –  Scotty Feb 1 '12 at 18:06

3 Answers 3

up vote 0 down vote accepted

I suppose that you know how to find variable $t$ (time) from system below :

$$\begin{cases} x + y = 30 \\ x=4\cdot t \\ y=7 \cdot t \end{cases}$$

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Yeah, it just clicked. thanks –  Scotty Feb 1 '12 at 18:09

Hint: at what speed is Kara approaching Ken?

A different way:

Let $x$ be the distance in miles that Kara has travelled when they meet. Note that at that time, Ken has traveled $30-x$ miles. The time it takes Kara to reach the meeting point is $x/7$. The time it takes Ken to reach the meeting point is the same as Kara's, but is also equal to $(30-x)/4$.

Solve for $x$, then for $t$.

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Here is another way. Ken is 4 and Kara is 7 so 4+7=11. Then it's just the simple matter of 30/11

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