## Bicycles

21

October

Ai and An, two Chinese sisters, were asked by their mother to take some food to their aging grandmother in another village 20 miles away. They could either walk the distance at a rate of 4 miles per hour or ride their bicycles at a rate of 8 miles per hour. Keen to get to their grandmother as quickly as possible they decided to ride. Unfortunately, after only 4 miles Ai suffered a tyre blow-out and had to abandon her bike at the side of the road. Assuming that turning back was not an option the sisters could now either walk together the remaining distance or one could walk while the other rode the remaining bike (the bike could not hold both of them together).

The course of action they decided on meant that they could get to their grandmother’s house as quickly as possible while minimising walking time.

What combination of walking and riding did they use?

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Ai rode the bike for 1 hour for a distance of 8 miles. Leaving the bike at the roadside she then walked the last 8 miles over 2 hours to her grandmother’s house. An walked for 2 hours, reached the bicycle, then rode the rest of the way arriving 1 hour later at the same time as Ai. In total it took 3 hours to travel the last 16 miles.

Ai rode the bike for 1 hour for a distance of 8 miles. Leaving the bike at the roadside she then walked the last 8 miles over 2 hours to her grandmother’s house. An walked for 2 hours, reached the bicycle, then rode the rest of the way arriving 1 hour later at the same time as Ai. In total it took 3 hours to travel the last 16 miles.

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I figured one would ride all the way, and grandma could eat while waiting for the other to get there.

Thanks Miss Cellania, your solution is certainly more beneficial for Grandma.

This doesn’t really minimize the walking time.

The total walking time is still 4 hours (each girl walks 2 hours)

Thanks for taking the time to comment.

It’s true that the sisters walk for a gross total of 4 hours which would have been the same if one had sat down by the bike and the other had walked on rather than ride. However, the puzzle does state that the sisters’ solution would get them there as quickly as possible while minimising walking time. The solution given allows them to get there in 3 hours rather than four.

My solution: Ai rides for 2 hours, traveling the remaining 16 miles, An would walk 8 miles. Ai drops off the food, turns around and rides for 40 minutes to meet An who kept walking. Ai is done, An rides to grandma’s with her food in 40 minutes. Total 3 hours, 20 minutes. This way takes a little longer, but there’s less walking (An walks 1 hour, 20 minutes, Ai doesn’t walk.)

I like it. Can’t help but feel a bit sorry for An though.

The problem should have stated that they had to arrive at Grandma’s house together. My solution was An just ride the bike with food, Ai goes back home walking and do some errand for An to compensate.

The puzzle asks you to assume that turning back is not an option. It was not a requirement of the puzzle that they had to arrive together. The fact that they did forms part of this solution but there may well be other acceptable solutions. Thanks for your comment.

I was thinking that one would go back home on the bike to get the repair kit while the other would continue walking. In a bit less than 2 hours, they would be together again with 2 working bikes reaching the destination in 3hours from the incident. It would then be far easier on the way back.

The puzzle states that you need to assume that turning back is not an option. Your solution also assumes that they own a repair kit. Thanks for commenting though – and I agree, getting home would be a pain.

have to agree with Miss Cellania