Jogging Around A Track

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llmr19230

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This is for a 6th grade advanced math class:

Dionne can run around a circular track in 120 seconds. Basha, running in the opposite direction as Dionne, meets Dionne ever 48 seconds. Sandra, running in the same direction as Basha, passes Basha every 240 seconds. How often does Sandra meet Dionne?

We have to show all work, all steps. Make a physical representation.

llmr19230

llmr19230@gmail.com
 
Dionne makes it around the track in 120 sec.
If Basha passes every 48 sec. then they pass 2 ½ times every rotation.

How do we know? How many 48 can occur in one 120? 48 goes into 120, 2.5 times.

Since Sandra and Basha are going in the same direction, Dionna passes both of them (Sandra first because she runs faster then Basha).
So each time Dionne passes S he then passes B (just with a bigger time gap).
Until the point that S overtakes B going in the same direction (which occurs in 240 sec.)

In the time it takes S to overtake B (240 sec.), D has gone around twice.
That means that D has passed B a total of 5 times ( because we've established that they pass 2.5 times each rotation ( in 2 rotations, it's 2.5 + 2.5 = 5 passes))

In this same time frame (240 sec. or 2 rotations) D will pass S one extra time ( or 6 times)

So to sum up what we have so far, in 240 sec. or twice around Dionne passes Basha 5 times and he passes Sandra 6 times.

So now lets get the rate for Sandra.

In 240 sec. she passes 6 times. 240 / 6 = 40.

Dionne passes Sandra every 40 sec. and Basha every 48 sec..


Sorry there is no picture representation. This is my first posting and I have not yet learned how to add images (like pie graphs). You can make a circle and cut it into 5ths. Label each fifth as 24 sec. since 2/5 represents 48 sec. ( 1/5 is half as much - 1/2 of 48 is 24)......

Hope this helps.




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That was allot of info crammed into paragraphs, which is sometimes hard to follow. If you need additional explanation to any part of this answer, just post it and I’ll try to explain it better.
 
Aloha Charlie:

It's easy to insert images into your posts here.

You have the choice of grabbing an image already on the Internet (eg: tinypic.com) using its URL or uploading an image from your hard drive to this site's server.

The BBCode tags [ img ] (URL GOES HERE) [ /img ] will snatch images from the Internet. Click the Img button, to insert the tags, or just type them. (There are no spaces within the square brackets; I had to insert those spaces to "inactivate" the tags for display purposes.)

I described uploading images to this site HERE and HERE.

You can also click on any post's
button (upper right corner), to see what the author typed to achieve any effect.

You can private-message me, if you have questions.

Cheers ~ Mark

MY EDIT: Fixed broken link.

Trying to!!
Click to expand...
 
Thanks Mark,
Your info is very helpful. I appreciate you taking the time to help out.
Have a great day, Charlie
 
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