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Question

In a race Karan covers 1m in 1st second, in the next second he covers twice the distance he covered in 1st second, in 3rd second he covers twice the distance which covered in 2nd second and he continues to run like this till six seconds. After that due to tiredness his speed keeps on going down, as in 7th second he covers only half the distance which he covered in 6th second and in 8thsecond he covers half the distance which he covered in 7thsecond and he continuous in that manner. If Karan completes the race in 9 seconds, find the length of given track. [4 MARKS]

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Solution

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Here are the distances covered by Karan in each second

1st second = 1m

2nd second =2m

3rd second = 4m

4th second = 8m

5th second = 16m

6th second = 32m

7th second = 16m

8th second = 8m

9th second = 4m

Length of the given track = (1+2+4+8+16+32+16+8+4) m

Length of the given track = 91 m


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