One cold winter day, a young woman finds herself alone near a frozen lake. Suddenly, a hooded thug appears from behind the trees holding a knife and demands all her money. In panic, she runs out over the frozen lake but finds that the lake is too slippery to run on - she can only walk fast...
Luckily for her, the thug is afraid to step on the ice (probably because of some traumatic childhood incident, I imagine). But he waits patiently around the edge of the lake always moving towards her.
Now begins the puzzle:
Assume the lake is perfectly circular with a radius of 1 mile exactly. The thug can run exactly 4 times as fast as she can walk on the ice. If she can get to the edge of the lake before the thug gets there, she can outrun him (she's in her college track team, you see). At the dead center of the fully frozen lake, there is a buoy.
Part 1 - Easy
a) How can she reach the edge of the lake quickest before the thug gets there?
b) How far will the thug be when she gets there?
Part 2 - Advanced
a) What strategy should she adopt to maximize the distance between her and the thug when she gets to the edge?
b) How much is this maximum possible distance (along the edge of the lake) ?
PS: She doesn't have a cell phone - so no wisecracks about calling 911 :-P And there is nobody else around to hear her scream for help!
Question
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One cold winter day, a young woman finds herself alone near a frozen lake. Suddenly, a hooded thug appears from behind the trees holding a knife and demands all her money. In panic, she runs out over the frozen lake but finds that the lake is too slippery to run on - she can only walk fast...
Luckily for her, the thug is afraid to step on the ice (probably because of some traumatic childhood incident, I imagine). But he waits patiently around the edge of the lake always moving towards her.
Now begins the puzzle:
Assume the lake is perfectly circular with a radius of 1 mile exactly. The thug can run exactly 4 times as fast as she can walk on the ice. If she can get to the edge of the lake before the thug gets there, she can outrun him (she's in her college track team, you see). At the dead center of the fully frozen lake, there is a buoy.
Part 1 - Easy
a) How can she reach the edge of the lake quickest before the thug gets there?
b) How far will the thug be when she gets there?
Part 2 - Advanced
a) What strategy should she adopt to maximize the distance between her and the thug when she gets to the edge?
b) How much is this maximum possible distance (along the edge of the lake) ?
PS: She doesn't have a cell phone - so no wisecracks about calling 911 :-P And there is nobody else around to hear her scream for help!
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