Two buses start from the same depot. Bus A goes 27 km West, then turns to its…

Concept: In a direction-sense problem, place the common starting point at the origin of an East-West / North-South coordinate system, with East and North as the positive axes. Track each moving object leg by leg, using the rule that a right turn rotates the current facing direction 90° clockwise (North → East → South → West → North). The relative position of one object with respect to another is then simply the difference between their final coordinates.

Application:

1. Take the depot as the origin (0, 0) for both buses, with East and North as the positive directions.

2. Bus A moves 27 km West: its position becomes 27 km West, 0 km North.

3. Bus A turns right — facing West, a right turn points it North — and moves 43 km: its position becomes 27 km West, 43 km North.

4. Bus B moves 19 km North: its position becomes 0 km West, 19 km North.

5. Bus B turns and moves 61 km West: its position becomes 61 km West, 19 km North.

6. Bus B turns right — facing West, a right turn points it North — and moves 24 km: its position becomes 61 km West, 19 + 24 = 43 km North.

Cross-check: comparing the two buses' final coordinates:

Both buses sit exactly 43 km North of the depot, so they lie on the same east-west line — the entire separation between them is therefore horizontal. Bus B's westward leg (61 km) exceeds Bus A's westward leg (27 km) by 34 km, so Bus B lies 34 km further west than Bus A.

Hence, Bus B is 34 km West of Bus A.