Question

A robot walks such that each step it takes is two-thirds of the previous step. Find the distance covered in 3 steps if the third step was $\frac{16}{27}m$.

• A. $2\frac{1}{3}m$
• B. $2\frac{22}{27}m$
• C. $2\frac{2}{9}m$
• D. $2\frac{1}{3}m$

Answer 1

The correct option is B $2\frac{22}{27}m$

Third step $=\frac{16}{27}m=\frac{2}{3}\left(\frac{8}{9}\right)m$ (here we have found the fraction which when multiplied with $\frac{2}{3}$ gives $\frac{16}{27}$)
Second step $=\frac{8}{9}m=\frac{2}{3}\left(\frac{4}{3}\right)m$
First step $=\frac{4}{3}m=1\frac{1}{3}m$
Total distance covered $=\frac{4}{3}+\frac{8}{9}+\frac{16}{27}$
$=\frac{4\times 9}{3\times 9}+\frac{8\times 3}{9\times 3}+\frac{16}{27}$
$=\frac{36+24+16}{27}$
$=\frac{76}{27}$
$=2\frac{22}{27}m$
Total distance covered by the robot is $2\frac{22}{27}m$.