Two buses leave the same station at 8:00 pm. One travels north at 30 kph and the other travels east at 40 kph. How many kilometers apart are they at 10:00 pm?

Two buses leave the same station at 8:00 pm. One travels north at 30 kph and the other travels east at 40 kph. How many kilometers apart are they at 10:00 pm?

• A. 140 km
• B. 100 km
• C. 70 km
• D. 50 km

Answer: (B)

When two travelers move in perpendicular directions from the same point, their separation forms a right triangle where each leg is the distance traveled in one direction. After two hours, the northbound bus has covered 60 km (30 km/h × 2 h) and the eastbound bus has covered 80 km (40 km/h × 2 h). The straight-line distance between them is the hypotenuse of that right triangle, so use the Pythagorean relation: sqrt(60^2 + 80^2) = sqrt(3600 + 6400) = sqrt(10000) = 100 km. They are 100 km apart. The other options arise from adding distances or misapplying arithmetic, but the correct geometry gives 100 km.

When two travelers move in perpendicular directions from the same point, their separation forms a right triangle where each leg is the distance traveled in one direction. After two hours, the northbound bus has covered 60 km (30 km/h × 2 h) and the eastbound bus has covered 80 km (40 km/h × 2 h). The straight-line distance between them is the hypotenuse of that right triangle, so use the Pythagorean relation: sqrt(60^2 + 80^2) = sqrt(3600 + 6400) = sqrt(10000) = 100 km. They are 100 km apart. The other options arise from adding distances or misapplying arithmetic, but the correct geometry gives 100 km.