Two pairs of friends are walking around the oval track in their schoolyard for an hour after school. they all begin at the beginning of the track and at the same time. the first pair takes 6 minutes to walk around the track once. the second pair takes 9 minutes to walk around the track once. a) after how many minutes will they meet again at the beginning of the track? b) if they walk for an hour, how many times will they meet at the beginning of the track? would be greatly appreciated.

a) The time after which they will meet again at the beginning of the part is the L.C.M. of their independent minutes to complete the walk around.

L.C.M of 6 and 9 is 18.

So, after 18 minutes, the first pair will complete 3 rounds and they will be at the beginning of the track and the second pair will complete 2 rounds and they will also be at the beginning of the track.

Hence, after 18 minutes, the two pairs will meet at the beginning of the track.

b) The number of times they will meet is the quotient when dividing 60 by 18.

Clearly, 18 goes 3 times in 60.

Hence, they will meet 3 times in one hour.

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