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 he covered in $2^{nd}$ second and he continues to run like this till six seconds. After that he slows 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

Application: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Here are the distances covered by Karan in each second

$1^{st}$ second = 1m

$2^{nd}$ second =$1\times 2$=2m

Hence, the length of the track is 2 m.

$3^{rd}$ second =$2\times 2$= 4m

$4^{th}$ second =$4\times 2$= 8m

$5^{th}$ second = $8\times 2$=16m

$6^{th}$ second = $16\times 2$=32m

$7^{th}$ second =$32÷2$= 16m

$8^{th}$ second =$16÷2$= 8m

$9^{th}$ second =$8÷2$= 4m

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

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

Hence, the length of the track is 91 m.