prompt: Darrel is an experienced tracker.  He can tell a lot about an animal by the footprints it leaves behind.  One day he saw a set of coyote footprints.  Based on the impressions, he could tell the animal was traveling east at 15 miles per hour, and that the animal left the prints 1 hour ago.  If the coyote continues to travel east at 15 miles per hour, and Darrell hops on his motorbike and travels east at 30 miles per hour, how long, in hours, will it take for Darrel to catch up to the coyote?
messages.content: Darrel is an experienced tracker.  He can tell a lot about an animal by the footprints it leaves behind.  One day he saw a set of coyote footprints.  Based on the impressions, he could tell the animal was traveling east at 15 miles per hour, and that the animal left the prints 1 hour ago.  If the coyote continues to travel east at 15 miles per hour, and Darrell hops on his motorbike and travels east at 30 miles per hour, how long, in hours, will it take for Darrel to catch up to the coyote?
messages.role: user
messages.content: If we let x be the amount of time, in hours, it will take for Darrel to catch up to the coyote, then we can figure this out.
  Because the distance Darrel travels is defined as the length of time Darrel travels (x) and Darrel's speed (20mph), or the expression 2*x.
  And the distance the coyote travels is defined as the length of time the coyote travels (x+1 hour) and the coyote's speed (15 mph), or the expression (x+1)*1.
  And since the distance Darrel and the coyote travel is the same, then 2*x=(x+1)*1
  Simplifying the expression, we get 2*x=x+1.
  If we subtract 1 x from each side, we get x=1, the amount of time in hours.
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messages.role: assistant