Question

$\text{Anna takes 600 equal steps, each measuring}1\frac{1}{2}\text{ft, to reach home from her school. If she}\text{wants to reach home in 660 equal steps,}\text{how big should each new step be?}$

• A. $1\frac{4}{11}\text{ft}$
• B. $1\frac{8}{11}\text{ft}$
• C. $2\frac{4}{11}\text{ft}$
• D. $2\frac{8}{11}\text{ft}$

Answer 1

The correct option is A $1\frac{4}{11}\text{ft}$

$\text{Length of each normal step}=1\frac{1}{2}\text{ft}$

$\text{Total number of normal steps needed to}\text{reach home}=600$

$⟹\text{Distance from school to home}=(600\times 1\frac{1}{2})\text{ft}$

$=[600\times \frac{(2\times 1)+1}{2}]\text{ft}$

$=[600\times \frac{3}{2}]\text{ft}$

$=\left[\frac{600\times 3}{1\times 2}\right]\text{ft}$

$=\frac{1800}{2}\text{ft}$

$=900\text{ft}$

$\text{Now, Anna wants to reach her home in}\text{660 steps:}$

$\therefore \text{She has to cover 900 ft in 660 steps}$

$⟹\text{Length of each new step}\times 660=900\text{ft}$

$\text{The corresponding division equation is:}$

$\text{Length of each new step}=900\text{ft}÷660$

$\text{Solving this equation, we find:}$

$900\text{ft}÷660$

$=\frac{900}{660}=\frac{900÷60}{660÷60}=\frac{15}{11}=1\frac{4}{11}\text{ft}$

$\therefore \text{Each of Anna's new step should be}1\frac{4}{11}\text{ft long for her to reach home in}\text{exactly 660 steps.}$