Two people start at the same point and walk 3 meters apart in opposite directions, then each turns right and travels 4 meters. How far apart are they?

Two people start at the same point and walk 3 meters apart in opposite directions, then each turns right and travels 4 meters. How far apart are they?

• A. 7
• B. 12
• C. 15
• D. 10

Answer: (D)

When two people move away from the same starting point in opposite directions, they stretch along a straight line. Each going 3 meters means they are 6 meters apart along that line. Then they each turn right and travel 4 meters. From their new directions, one moves perpendicular to the line in the south direction and the other in the north direction, so their vertical separation becomes 8 meters (one ends 4 meters below the line, the other 4 meters above). Visualize their final positions: they are 6 meters apart horizontally and 8 meters apart vertically. The direct distance between them is found with the Pythagorean theorem: sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10 meters. So the final separation is 10 meters.

When two people move away from the same starting point in opposite directions, they stretch along a straight line. Each going 3 meters means they are 6 meters apart along that line. Then they each turn right and travel 4 meters. From their new directions, one moves perpendicular to the line in the south direction and the other in the north direction, so their vertical separation becomes 8 meters (one ends 4 meters below the line, the other 4 meters above).

Visualize their final positions: they are 6 meters apart horizontally and 8 meters apart vertically. The direct distance between them is found with the Pythagorean theorem: sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10 meters. So the final separation is 10 meters.