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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