can you solve the speedy fly problem? without seeing the answer?

Question

A Ferrari is traveling at 30 miles per hour on a head-on collision course with a Maserati, which is being driven at a leisurely 20 miles per hour. When the two cars are exactly 50 miles apart, a very fast fly leaves the front fender of the Ferrari and travels towards the Maserati at 100 miles per hour. When it reaches the Maserati, it instantly reverses direction and flies back to the Ferrari and continues winging back and forth between the rapidly approaching cars. At the moment the two cars collide, what is the total distance the fly has covered?
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{Solution}

At first glance it may seem that a horrendous calculation is necessary to solve this: the sum of an infinite series of numbers that get smaller and smaller as the cars approach each other. But if you focus on time rather than distance, a solution is easy. The cars are 50 miles apart and traveling towards each other at a combined speed of 50 miles per hour, so they will meet in one hour. In that hour, a fly that flies at 10

Answer 1

Thanks.

Answer 2

relative speed =30+20=50mph
distance=50 miles
time for them to close up 50 miles=1 hour
speed of the fly=100 mph
distance travelled by the fly=1*100=100 miles

Answer 3

The fly covers a hundred miles. There's a funny story about Claude Shannon (a famous mathematician at Bell Labs in the 30's, 40's and 50's). He was asked that question at lunch one day by a co-worker. Shannon thought for a moment and said, "One hundred miles." The co-worker said something about most people would have used the sum of an infinite series. Shannon looked at him and said, "But that *is* the way I did it." ☺


Doug

Answer 4

Hi. Not horrendous. The time the fly is air born is equal to the time the cars are traveling towards each other. The speed is known. Can you solve it now?

Answer 5

yes.