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October 29th, 2010, 08:29 PM  #1 
Newbie Joined: Oct 2010 Posts: 1 Thanks: 0  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? 
October 29th, 2010, 09:04 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  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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