How can I calculate the time two people will meet if they are paddling towards each other on a lake?

Question

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?

Answer 1

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

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

Answer 2

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 $t$.