Direction-distance puzzle on a main road: Compute the separation between two cars after detours and a partial breakdown. Road setup: Two cars start from opposite ends of the same straight main road, 150 km apart. Car 1 drives 25 km along the main road, turns right for 15 km, turns left for 25 km, then returns back to the main road. At the same time, Car 2 (from the other end) manages to cover only 35 km along the main road due to a minor breakdown. Find the distance between the two cars when Car 1 re-enters the main road.

Given data

• Total initial separation along the main road = 150 km
• Car 1 path: 25 km on road → right 15 km (off-road) → left 25 km (parallel to road) → back to main road (perpendicular)
• Car 2 covers 35 km along the main road toward Car 1

Concept/ApproachResolve Car 1's off-road motion into components. Only the east–west (along-road) component affects along-road separation. Returning to the main road restores the perpendicular offset (15 km) back to zero.

Step-by-step calculationTake Car 1 start at x = 0; Car 2 start at x = 150 (same x-axis = main road).Car 1: +25 km (to x = 25) → right 15 km (perpendicular) → left-turn +25 km (to x = 50) → return perpendicular 15 km to the road at x = 50.Car 2: −35 km from x = 150 → x = 115.Separation on the road = 115 − 50 = 65 km.

VerificationPerpendicular excursions cancel out when Car 1 comes back to the road; only along-road displacements matter.

Common pitfalls

• Adding the 15 km perpendicular leg into the final distance (it cancels when rejoining the road).
• Forgetting Car 2's 35 km progress reduces the initial 150 km.

Final Answer65 km