Answers - May

Answers for Rebus post

1. Last laugh
2. Once in a blue moon
3. Once upon a time
4. Middle of nowhere
5. Forever a day
6. Get back to work
7. Just in time
8. Call a spade a spade
9. Time up
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Answer for Distance puzzle

Total distance traveled by soldier X is '20(2+sqrt(2))'
The sequence of diagrams below will help understand the solution better
Green line gives position of the battalion at a given time.
X, A and HQ gives the position of soldier, captain and Head Quarters respectively
All units are in miles

Stage 1: Distance traveled by Soldier = 0


Stage 2: Distance traveled by soldier = 20 + a
When soldier X meets captain A, the battalion would have covered a distance 'a' of the 20 miles towards their HQ. So X should have run the extra 20 miles from the end of the line to the beginning


Stage 3: Distance traveled by soldier = 20 + 2a
When X returned to his original position, A reached the HQ, meaning that they have covered the remaining distance (20-a). So, X should have run a miles in opposite direction in that time.

Stage 4 (last): Total distance traveled by soldier = 20 + 2a + 20
Having reached his original position, now X has to march another 20 miles to reach the HQ

Hence, X has traveled a distance of 40 + 2a miles in total
To find a: Use relative distance traveled by X and rest of the battalion
(20 + a)/a = a/(20-a)
Gives a = 20/sqrt(2)
So,
40 + 2a = 20 (2 + sqrt(2))