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=Quick Thinking Tests=

Q:
A band is walking in the street with a constant speed. Someone in the last raw has a dog. The dog runs ahead, reaches the front line of the band and gets back to it's owner. The dog's speed was also constant all the way and while it was running the band passed 50 feet. Find the length of the dog's path,if the distance between the front and the rear line of the band is 50 feet.

solution by Arif:
ITS SIMPLE what if band was still and was not moving ... what's the distance dog has traveled ...

50*(JOURNEY TO FRONT ROW) + 50*(JOURNEY BACK TO lastrow)....SO IS 100
now that band is not still and it also has moved 50 feet... so dog also would have traveled that 50 ... on it's way...so final answer is simply
= 100+ 50 = 150

means the = 2*distance between first row and last row ( 50) + distance traveled by band

hint from Hitequest:
while band went x ahead dog ran 50+x, while band went 50-x dog ran x
x/(50+x) = (50-x)/x
x*x = (50-x)*(50+x)
x*x = 2500-x*x
x=35

correction by Randy L:
x - is a bit more than 35

from alan:
while the math of solution 2 seems to be correct, 35 - doesn't make sense to me since the length of the band is 50?

Swati:
The solution provided by HITEQUEST is right.
A little correction is that x comes out to be 35.35 and dog travels a total path of (50 + 35.35) = 85.35