A courier travels between three cities—Alpha, Beta, and Gamma—in a single closed loop, visiting each city once before returning to the starting point. The trip from Alpha to Beta takes twice as long as the trip from Beta to Gamma. The trip from Gamma to Alpha takes 3 hours, which is 1 hour longer than the trip from Alpha to Beta. How long is the entire loop?
10.5 hours
Let Gamma to Alpha = 3 hours. We are told this is 1 hour longer than Alpha to Beta, so Alpha to Beta = 2 hours. Alpha to Beta (2 hours) is twice as long as Beta to Gamma, so Beta to Gamma = 1 hour. Total loop time = 3 + 2 + 1 = 6 hours? Wait, let's re-add: Gamma-Alpha (3) + Alpha-Beta (2) + Beta-Gamma (1) = 6 hours. Let's check the wording: 'The trip from Alpha to Beta takes twice as long as the trip from Beta to Gamma.' If Alpha-Beta is 2, Beta-Gamma is 1. Total = 3 + 2 + 1 = 6 hours.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Easy. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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