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| The slug and the snail (Posted on 2008-10-27) |
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A slug and a snail decided to settle a long-standing argument as to who was the best sprinter. So they planned a race between two stones set a distance D cm apart. Said the slug to the snail:
- "Since I'm slimier than you, I intend to start T seconds before you".
- "In that case," said the snail, who was rather slow, "I'm going to give you X cm start" (the snail stays at the stone, and the slug starts from X cm ahead.)
It didn't matter. The slug, who could move at speed V cm/sec, was only half as fast as the snail. The result was a dead heat, t seconds after the slug set off.
Now, D, t, T, V and X were all whole numbers from 1 to 10 inclusive, no two numbers being the same.
How long did it take the snail to reach the finish?
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Submitted by pcbouhid
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Solution:
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The snail reached the finish in 5 seconds.
Since they reach the same position D at the same time t we have:
2V(t - T) = X + Vt = D.
Rearrangement gives V(t - 2T) = X.
Any solution where t = 2T + 1 cannot work since then V = X (must be different numbers).
For the set of solutions where T = 1, t = 4, 5, 6 and D = 6V, 8V, 10V, respectively, only V=1 allows D less than 10 but then V = T = 1 (invalid).
For T = 2, t = 6, 7 and D = 8V, 10V, respectively. Again V = 1 which gives X = 2 for t = 6 (T = X invalid) and X = 3 for t = 7 with D = 10, a valid solution.
For T = 3, t = 8 and D = 10V. Here, V = 1 gives X = 2 with D = 10, another valid solution.
So there are two valid solutions, both with V = 1 and D = 10, with (T, t) = (2, 7) and (3, 8). In both cases t - T = 5. |
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