A column of soldiers, marching at 120 paces per minute, keep in step with the beat of a drummer at the head of the column. It is observed that the soldiers in the rear end of the column are striding forward with the left foot when the drummer is advancing with the right foot. What is the approximate length of the column?

Question

baru · Answer

i dont get it

first part says " they keep in step with the beat of a drummer at the head of the column. "

then it says, that there is a mismatch in their footing...? how can that be?

ganeshie8 · Answer

guess we need to consider the time taken by sound to reach the soldiers in the back..

bemoseemo · Answer

Sound travels at 340 meters per second, only 3 football fields a second.

baru · Answer

O.O i was about to guess that...but we dont know how much "a pace" measures

baru · Answer

120 paces/min

bemoseemo · Answer

The pace is an uncommon US customary unit of length denoting a brisk step and equal to 2½  feet or 30  inches (75.2  cm).

baru · Answer

oh

ganeshie8 · Answer

I am also not sure... 2.5 feet looks good to me...

ganeshie8 · Answer

Answer given is 170 meters

baru · Answer

first we can consider what happens to a soldier 1m away from the drummer,

we can calculate how long sound takes to reach him, 
so he starts that many seconds late

ganeshie8 · Answer

time = distance / speed = distance / 340

baru · Answer

aagh...i getting missed up...i'm starting to think we dont need to know how much a pace is

baru · Answer

*messed

baru · Answer

yes, we dont need what a pace is,

1m away guy starts 1/340 sec late

column marches 2paces/sec  (read pace as steps)

so when the time lag reaches 1/2 second, there is a perfect mismatch of footing

baru · Answer

1/340 * x = 1/2

x= 170

baru · Answer

(guy x meter away starts x/340 seconds later)

ganeshie8 · Answer

Nice! I think length of the column could be any odd multiple of 170

baru · Answer

yep,
you said 1pace =2.5 ft just to throw me off dint u? XD

baru · Answer

anyways, i can sleep in peace now. nice question.. thanks and goodnight :)

ganeshie8 · Answer

Hahaha yes somewhat... but I really had no clue initially! have good sleep :)