A marching band is 50m long. A dog starts running from the back of the band to the front, then turns round and runs to the back of the band. During this time, the band moves forward by 50m. Band and dog both move at constant speeds. What is the dog's speed?
2006-12-04 05:08:23 · 3 answers · asked by mongrel 1 in Science & Mathematics ➔ Mathematics
data insufficiency
2006-12-04 05:13:25 · answer #1 · answered by raj 7 · 0⤊ 0⤋
The dog must be going [1 + sqrt(2)] or 2.414 times the speed of the band. Here is an example of how it works. Suppose the band is travelling at 50 meters/minute. Then the dog must travel 2.414*50 or 120.71 meters/minute. In 0.707 minutes, the band will have travelled 50*0.707 = 35.35 meters. In this time, the dog wll have run 120.71*0.707 = 85.35 meters. Notice that the dog has travelled 50 meters farther than the band, which puts him at the front. Now the dog turns around and runs back. After (1 - 0.707) or 0.293 minutes, he has run 120.71*0.293 = 35.35 meters. In ths time, the back of the band has advanced 50*0.293 = 14.65 meters. The dog's distance + the bands distance = 35.35 + 14.65 = 50 meters, so the dog has reached the back of the band as required. The total time for this is 0.707+0.293=1 minute.
2006-12-04 14:45:35 · answer #2 · answered by heartsensei 4 · 0⤊ 0⤋
All we can say is that the dog 's speed is twice that of the band.
2006-12-04 13:27:11 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋