Question

Rachel lives $5\frac{3}{4}$ miles away from her school. In the morning, she covers $5\frac{1}{2}$ miles by foot and the remaining distance by local bus. Find the square of the distance covered by Rachel by local bus.

• A. $\frac{1}{8}$ km
  
• B. $\frac{1}{32}$ km
  
• C. $\frac{1}{4}$ km
  
• D. $\frac{1}{16}$ km
  

Answer 1

The correct option is D $\frac{1}{16}$ km


$\bullet$ Distance between Rachel's home and her school $=5\frac{3}{4}$ km $=\frac{(5\times 4)+3}{4}=\frac{23}{4}$ km
$\bullet$ Distance covered by Rachel by foot $=5\frac{1}{2}$ km $=\frac{(5\times 2)+1}{2}=\frac{11}{2}$ km

$\therefore$ Distance covered by Rachel by local bus $=$ Total distance $-$ Distance covered by foot
$=(\frac{23}{4}-\frac{11}{2})$ km

Taking the L.C.M of $4$ and $2,$ and then solving, we get:
$=(\frac{23-22}{4})\text{km}=\frac{1}{4}\text{km}$

Hence, the distance covered by Rachel by local bus $=\frac{1}{4}$ km.

We need to find the square of distance covered by Rachel by local bus.

Square of distance covered by Rachel by local bus $=(\frac{1}{4}{)}^2\text{km}$ $=\frac{1}{16}$ km

Therefore, option (d.) is the correct choice.

$\underset{–}{\text{Note:}}$
$\frac{1}{4}$ is a proper fraction as numerator $\left(1\right)$ is less than the denominator $\left(4\right).$ We know that the square of a proper fraction is always less than the fraction itself. Hence, $(\frac{1}{4}{)}^2<\frac{1}{4}\Rightarrow \frac{1}{16}<\frac{1}{4}.$