Two cars 200 miles apart are moving toward each other,each one is going at a speed of 50 miles per hour.A hornet starting on the front of one of them flies back and forth between them at a rate of 75 miles per hour.It does this until the cars collide and crush the hornet to death. What is the total distance the hornet has flown?

Each car will travel 100 miles at 50 mph and the collision will occur in two hours. In those two hours, assuming a constant speed of 75 mph, the hornet will fly 150 miles.
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08-06-02, 10:50 PM
coldfuse
Each car will travel 100 miles at 50 mph and the collision will occur in two hours. In those two hours, assuming a constant speed of 75 mph, the hornet will fly 150 miles.

08-07-02, 12:17 AM
mozart56
POOR HORNET .....150 miles it is !

08-07-02, 11:43 AM
Professor
This is an old classic puzzle, which I originally heard as the problem of a bee flying between oncoming railroad trains.

If you're not as clever as Coldfuse wink you could try to set it up as a complicated sum of a series, computing each segment of flight individually.

Of course this will eventually yield the correct answer, but the trick is to realize that if the hornet is flying at a constant speed, then you can simply find the total time of flight to get the total distance.

08-07-02, 01:00 PM
WiteoutKing
fast hornet too...

08-08-02, 09:33 AM
MiranndaGrey
confused I've never been particularly adept at calculating these sorts of time, distance, rate questions. Would anyone mind solving the problem by showing their work?

08-08-02, 01:31 PM
frankvan
200mi/2=100 (distance each train must travel to meet since both travel at same rate) 100mi/50mph=2 hours, time it takes for the two trains to meet. Hornet flying at a constant speed of 75mph for 2 hours flies 75mph x 2 hrs= 150 miles. QED (quite easily done) wink

08-08-02, 04:24 PM
maiku
Hmmmm. According to my calculation, the hornet is squashed flat the first time it flies at 75 mph into a car traveling at 50 mph in the opposite direction. Since the hornet and the car approach each other at a relative speed of 50 mph+75 mph =125 mph (neglecting relativistic rules for the composition of velocities, of course) and are initially 200 miles apart, it will take 200/125 = 1.6 hours, or 1 hour and 36 minutes before the hornet gets creamed. smile

08-09-02, 12:47 PM
frankvan
Hmmm Maiku According to my calculations, in 1.6 hours there is still 40 miles of open space for my hornet to fly back and forth in, and he is still fast enough to outrun either one. No one says he has to fly into them before they meet. Am I wrong ?

08-09-02, 02:17 PM
maiku
Sorry, Frank, but you are wrong in this case. The question presumed that the hornet flies at a constant speed of 75 mph. Therefore it cannot (poor creature) avoid a fatal collision on its very first encounter with the oncoming car.

Think about the acceleration/deceleration required to land the hornet safely. Can't happen at a constant speed, can it?

Ignoring this problem, Coldfuse's solution is of course entirely right, simple, and elegant, as the Professor also points out. I posted what I did only because I wondered myself why anyone might think it was a problem you couldn't quite easily work out in your head. I hope there's some use for irony, even in the math forum. wink

08-09-02, 06:43 PM
WiteoutKing
Very clever, maiku, wouldn't have thought of that one myself.

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