Question

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

Answer 1

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

Here are the distances covered by Karan in each second

$1^{st}$ second = 1m

$2^{nd}$ second =2m

$3^{rd}$ second = 4m

$4^{th}$ second = 8m

$5^{th}$ second = 16m

$6^{th}$ second = 32m

$7^{th}$ second = 16m

$8^{th}$ second = 8m

$9^{th}$ second = 4m

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

$\Rightarrow$Length of the given track = 91 m