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Nancy's 100th Birthday

Nancy was born in California and is a bit crazy about running. She started running at the age of 4 years, and she is determined to run till she grows 100 years in age. As soon as she grew 4, she started running straight in a direction from the place she was born, but she also wants to celebrate her 100th birthday at her hometown. So, she decides that she will run till a particular point and will return back along the same path. But with age, the speed of Nancy decreases. In fact, it is directly proportional to the number of years left to reach 100 years of age. At the age of 52, she was running at 96km/year. Keeping all these constraints in mind, she wants to run as far as she can. Can you help her in finding out the farthest point she can reach?

SOLUTION : Going by proportionality relation(at age of x years), we can write speed = k(100-x), where k is a constant. At 52, speed = 96km/year. Using this, we get k = 2.

So, when Nancy is 4 years old, she will run at 192 km/year. At 5, she will run at 190 km/year and so on. From 4 years to 100 years, she can run 192+190+188+186+.....+2 = 9312 kms. SO, she can go till a farthest point of 9312/2 = 4656 kms.

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