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Solution to Fortnightly Challenge, Feb 3-16, 2024

Congratulations to Unnathi Rapaka, 8th Grade, The Global Edge School, Madhapur, Hyderabad for sharing a very elegant solution to this challenge!! This is the solution she came up with by discussing with friends and family.

Don't get discouraged if you found it difficult to solve the problem, or to understand the solution shared above. Sometimes one has to keep working on a problem for a long time before one is able to solve it or understand the solution! And this is completely worth it- because your brain is like a muscle- the more you exercise it, the stronger it will get. There are other ways to arrive at the solution- try and share your answers in the comments.

We are sharing the original question below for easy reference.


The Question

Once upon a time, a long time ago, a lady used to go to work by train every day. Unfortunately, the train station was a little far from her house and her husband would drop and pick her up by car.

Every evening, she would reach the train station at the same fixed time. The husband also would reach the train station with the car at exactly that same time. And then they would drive back home immediately.

One day, the lady got done at work early, took an earlier train back and reached the station 1 hour before her normal time. Instead of waiting at the train station, she started walking towards home.

After some time of walking, she saw her husband coming towards her in the car. (He did not know she had come early; there had been no communication between them because they both had Vodafone.) Her husband saw her, stopped, picked her up, took a U-turn, and they drove back.

This day, the lady reached home 20 minutes earlier than her normal time.

What is the ratio of the speed of the car to the lady's walking speed? 

Assume that she and the car both move at uniform/constant speeds.

It seems like there is not enough information given to solve this problem, but trust me, there is. You get extra points if you are able to answer this question without using algebra!

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