Question

The positions of two cities A and B are represented on the number line, where each consecutive integer represents the distance (in miles). What is the distance between the two cities A and B in miles?

• A. $2\frac{1}{3}$ miles
• B. $2\frac{5}{6}$ miles
• C. $2\frac{2}{3}$ miles
• D. $2\frac{1}{6}$ miles

Answer 1

The correct option is C $2\frac{2}{3}$ miles

The gap between two integers is divided into $6$ equal parts. Each division on the scale corresponds to $\frac{1}{6}$ mile.
A is $-11$ divisions from $0$ and point B is $5$ divisions from $0.$
Therefore,

Position of city $A=-\frac{11}{6}$ miles

Position of city $B=\frac{5}{6}$ miles

Distance between A and B = |Position of A - Position of B|

Distance between A and B $=|-\frac{11}{6}-\frac{5}{6}|$

$=|-\frac{16}{6}|$

$=|-\frac{8}{3}|=|-2\frac{2}{3}|$

$=2\frac{2}{3}$ miles

Distance between A and B is $2\frac{2}{3}$ miles.