Achilles and the Tortoise are running a race.
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Achilles and the Tortoise are running a race. Since the Tortoise is much slower than Achilles, Achilles decides to give him a head start of 20 seconds. If Achilles catches up to the Tortoise 1 min after Achilles started the race, what is the ratio of the speed of the Tortoise to the speed of Achilles?
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Show answer & explanation
The tortoise runs for 20 + 60 = 80 seconds, while John runs for 60 seconds over the same distance. The ratio of speeds is 60/80 = 3:4.
Step-by-step Derivation:
Step 1: Let speed of Tortoise be S_t and speed of John be S_j.
Step 2: Tortoise runs for head start (20 s) + chase time (60 s) = 80 s.
Step 3: John runs for 60 s.
Step 4: Distances are equal: S_t * 80 = S_j * 60 => S_t / S_j = 60 / 80 = 3 / 4 = 3:4.