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## Bike Trip

Math brain teasers require computations to solve.

 Puzzle ID: #3351 Fun: (2.53) Difficulty: (1.95) Category: Math Submitted By: 204_BLaZe_41 Corrected By: cnmne

Justin Time was on a gruelling trip from his hometown of Neutron to the town of Proton. Justin and his bicycle were able to hitch a ride to the town of Electron, which was exactly halfway to Proton. The ride lasted one hour, and was ten times faster than if Justin had cycled the same distance. When Justin got out of the car at Electron he noticed his tire was flat, which meant walking the rest of the way to Proton. Walking took him twice as long as cycling. When Justin finally reached Proton, he repaired his bicycle tire and rode the entire distance home to Neutron. How much time did each trip take and which of the two was faster?

The return trip was faster. Since it was one hour to Electron by car, which was ten times faster than cycling, the time from Electron to Proton took an additional 20 hours since he walked, and walking took twice as long as cycling. Therefore, the first half of the trip took a total of 21 hours. The return trip took Justin 20 hours, since he cycled the entire distance and cycling is twice as fast as walking.
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 Beelzebub Apr 10, 2002 That's a long way to walk or cycle. He should invest in a car. emilymonkeymaia Apr 12, 2002 I agree with Beelzebub. He should invest a car!!!! Dina_2002 May 11, 2002 it isnt relevant you guys!!! SandPman May 12, 2002 If it was uphill going and downhill coming back, he would be even faster on the return trip - or with the wind behind him. Only kidding! pizzahead May 14, 2002 There's an easy way to look at this. The second half of his trip (2*rate*1/2, or 1*rate) took exactly the same as the trip home. Since that's only half the trip, the trip home must be faster.