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

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?

• How much closer to each other are they after one hour? Commented Feb 1, 2012 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 Commented Feb 1, 2012 at 18:06

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

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

• Yeah, it just clicked. thanks Commented Feb 1, 2012 at 18:09

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

• Needs some elaboration. The version of August isn’t an answer, only a math woo. Commented Dec 8, 2014 at 11:32

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 $t$.

You can use relative velocities, the difference between their velocities is 3mph, and the distance is 30 miles, so it would take 10 hours for them to cover the same distance.

• Problems with English preposition “towards”? Commented Dec 8, 2014 at 11:23