Directions (79-81): Answer the questions based on the information given below.

Seven delivery agents P, Q, R, S, T, U, and V are parked at different spots in a logistics hub. S is 14m west of T, who is 10m west of V. R is east of S. The distance between V and S is twice the distance between R and S. U is 16m north of R. P is 12m east of U. P is 10m north of Q.

What is the shortest distance between R and V?

The correct answer is 12m.

Step-by-step explanation:

Step 1: Determine the distance between S and V.
We are given:
- S is 14m west of T.
- T is 10m west of V.

Since S, T, and V lie along the same horizontal (East-West) line in order from West to East (S → T → V), the total distance between S and V is:

$\text{Distance(S, V)}=\text{Distance(S, T)}+\text{Distance(T, V)}$

$\text{Distance(S, V)}=14\text{m}+10\text{m}=24\text{m}$

Step 2: Calculate the distance between R and S.
We are given that R is east of S, and the distance between V and S is twice the distance between R and S.

$\text{Distance(V, S)}=2\times \text{Distance(R, S)}$

Substituting Distance(V, S) = 24m into the equation:

$24\text{m}=2\times \text{Distance(R, S)}$

$\text{Distance(R, S)}=\frac{24\text{m}}{2}=12\text{m}$

Since R is east of S, R is positioned 12m to the east of S along the horizontal line.

Step 3: Find the shortest distance between R and V.
Both R and V lie on the same horizontal line to the east of S, with R being 12m east of S and V being 24m east of S.

$\text{Distance(R, V)}=\text{Distance(S, V)}-\text{Distance(R, S)}$

$\text{Distance(R, V)}=24\text{m}-12\text{m}=12\text{m}$

Therefore, the shortest distance between R and V is 12m.