My Math Forum Word speed problem

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 December 14th, 2009, 03:57 PM #1 Member   Joined: Oct 2009 Posts: 39 Thanks: 0 Word speed problem Two trains are moving towards each other, each traveling 75 mph. When the trains are 500 miles apart, a hawk starts flying back and forth between them (as soon as it gets to one train it turns around and flies back to the other). If the hawk can fly at a speed of 90 mph how far will the hawk have flown when the trains meet? Thanks.
 December 14th, 2009, 04:52 PM #2 Senior Member   Joined: Dec 2009 From: Las Vegas Posts: 209 Thanks: 0 Re: Word speed problem Hi alikn; 500 / 150 * 90 = 300 miles the hawk flies.
December 15th, 2009, 10:37 AM   #3
Math Team

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From: Lexington, MA

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Re: Word speed problem

Hello, alikn!

Quote:
 Two trains are moving towards each other, each traveling 75 mph. When the trains are 500 miles apart, a hawk starts flying back and forth between them (as soon as it gets to one train it turns around and flies back to the other). If the hawk can fly at a speed of 90 mph, how far will the hawk have flown when the trains meet?

This is a classic (very old) problem ... with a surprisingly simple answer.

$\text{The trains are approaching each other at a combined speed of 150 mph.}$
$\text{(It is as if one train is stopped and the other is approaching at 150 mph.)}$

$\text{To travel 500 miles, the trains take: }\:\frac{500}{150} \:=\:3\frac{1}{3}$$\text{ hours.}$

$\text{The hawk flies at 90 mph for }3\frac{1}{3}$$\text{ hours.}$
$\text{Therefore, it flies: }\;90\,\times\,3\frac{1}{3} \:=\:300\text{ miles.}$

 December 15th, 2009, 02:23 PM #4 Member   Joined: Oct 2009 Posts: 39 Thanks: 0 Re: Word speed problem Thank you very much for the help.

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