A Brain-Teaser: [Square convoy]
From The Sunday Times, 2nd January 1949 [link]
Four ships in convoy are at the corners of a square with sides one mile long. Ship B is due north of A; C is due east of B, and D is due south of C. The four ships are each sailing north at 10 miles per hour. A motor-boat, which travels at 26 miles per hour, starts at A, delivers a message to B, then to C, then to D, and finally returns to A. The distances between the ships are traversed by the shortest possible routes, and no allowance need be made for time taken in turning.
How far does the convoy advance whilst the motor-boat is going round?
This is earliest of the occasional Holiday Brain Teasers published in The Sunday Times prior to the start of numbered Teasers in 1961 that I have found. Prizes of 10 guineas and 5 guineas were awarded.
This puzzle was originally published with no title.
[teaser-1949-01-02] [teaser-unnumbered]
S2T2 
Jim Randell 9:16 am on 26 December 2021 Permalink |
(1) A to B:
The position of the motorboat is given by: 26t
And the position of B is given by: (1 + 10t)
These coincide when:
(2) B to C:
The motorboat travels along the hypotenuse of a right-angled triangle, a distance: 26t.
And C travels along another side, a distance: 10t.
The remaining side being of length 1.
(3) C to D:
The motorboat’s position is: −26t.
D’s position is: −1 + 10t.
(4) D to A:
A mirror image of B to C.
So the total time taken is:
And the distance travelled by each boat in the fleet:
Solution: The distance travelled by the fleet was 1 mile, 1295 yards, 20 inches.
LikeLike