Question

In the figure above, the usual route from Town $A$ to Town $D$ is indicated by the solid line. The broken line indicates a detour route from $B$ to $C$ through $E$. Each line segment is labeled with its length in miles. How many more miles is the trip from Town $A$ to Town $D$ via the detour than via the usual route?

• A. $4$
• B. $8$
• C. $10$
• D. $12$
• E. $18$

Answer 1

The correct option is B $8$

Trip from Town $A$ to Town $D$ via the usual route,

Number of miles via usual route $=$ Sum of the length of the paths in the usual route

$=$ $\left(AtoB\right)$ $+$ $\left(BtoC\right(usualroute\left)\right)$ $+$ $\left(CtoD\right)$

$=$ $(3$ $+$ $2)$ $+$ $(2$ $+$ $2)$ $+$ $(1$ $+$ $2)$

$=$ $5$ $+$ $4$ $+$ $3$

$=$ $12$

Number of miles via usual route $=$ $12$

Trip from Town $A$ to Town $D$ via the detour route,

Number of miles via detour route $=$ Sum of the length of the paths in the detour route

$=$ $\left(AtoB\right)$ $+$ $\left(BtoE\right(detourroute\left)\right)$ $+$ $\left(EtoC\right(detourroute\left)\right)$ $+$ $\left(CtoD\right)$

$=$ $(3$ $+$ $2)$ $+$ $(1$ $+$ $2$ $+$ $3)$ $+$ $(2$ $+$ $2$ $+$ $2)$ $+$ $(1$ $+$ $2)$

$=$ $5$ $+$ $6$ $+$ $6$ $+$ $3$

$=$ $20$

Number of miles via detour route $=$ $20$

Difference between the two routes $=$ Number of miles via detour route $-$ Number of miles via usual route

$=$ $20$ $-$ $12$

$=$ $8$

Therefore, number of miles from Town $A$ to Town $B$ via the detour route is ${}^{\prime }{8}^{\prime }$ miles more than usual route.