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.