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-   -   Distance/Rate ?? (http://mymathforum.com/algebra/15397-distance-rate.html)

mrjames October 29th, 2010 08:29 PM

Distance/Rate ??
 
Joe & Bill live 20 miles apart. At 9, Bill and Joe each take off on their bicycles riding toward each other, Bill at 8 miles an hour, and Joe at 7 miles an hour. At the moment Bill leaves, a fly leaves from Bill's handlebars and flies at 10 miles per hour to Joe's handlebars, then returns immediately to Bill's handlebars, and keeps going back and forth between the bikes until Joe & Bill meet.

How far did the fly fly?

MarkFL October 29th, 2010 09:04 PM

Re: Distance/Rate ??
 
The fly flies at 10 mph the entire time Bill and Joe are traveling , so we merely need to find how long it takes Bill and Joe to meet, time = t.

Let x be the distance Bill travels, and y be the distance Joe travels. This gives us:

x + y = 20

using distance = speed*time, we have

8t + 7t = 20

Combine like terms.

15t = 20

Solve for t.

t = 4/3

Let d be the distance for the fly, and use again distance = speed*time:

d = (10 mph)(4/3 hr) = 40/3 miles.


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