erikvm wrote:

Hey,

I found this question through Khan Academy, it goes as follows:

"A jogger and a walker set out at 9am from the same point, headed in the same direction. The average speed of the jogger is 1 mph slower than twice the speed of the walker. In two hours, the jogger is 3 miles ahead of the walker. Find the rate of the jogger"

Can someone please explain how I'd go about setting this up, preferably in a "Rate * Time = Distance" chart.

Thanks in advance

Dear Erik

In Distance-Speed problems, like in most Word Problems, if you're not so sure about how to go setting up the solution, a good first step is Visualization.

Make the given information come alive in a diagram, and often, you'll be able to see (literally!) what your next step should be.

Like, here is a visual representation of the information in this question:

Let's assume the Jogger's speed is J mph and the walker's speed is W mph. They both start from the same point at the same time. So, we show this common starting point with the dotted gray line. Now, 2 hours later, the jogger is 3 miles ahead of the walker. We've shown the snapshot of 2 hours later with the dotted black line.

Now, what does the diagram tell you?

(Distance traveled by Jogger in 2 hours) = (Distance traveled by Walker in 2 hours) + 3

Distance = Speed*Time

So, the above equation can be written as:

J*2 =

W*2 + 3 . . . (1)

This is equation 1 between the 2 unknowns. To find a unique value of j, we need another equation.

And that comes from the fact that

**Quote:**

The average speed of the jogger is 1 mph slower than twice the speed of the walker.

So,

the key takeaway of our discussion:

Representing the given information visually is a great first step in Word ProblemsHope this helped!

- Japinder

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