Two cyclists start from the same point at the same time: one north at 18 km/h and the other south at 20 km/h. After how long will they be 95 km apart?

Introduction / Context:When two objects move in opposite directions along a straight line, their separation grows at the sum of their speeds. This yields time directly from distance = rate * time.

Given Data / Assumptions:

• Cyclist A speed = 18 km/h (north).
• Cyclist B speed = 20 km/h (south).
• Desired separation = 95 km.

Concept / Approach:Relative separation speed = 18 + 20 = 38 km/h. Then time t = distance / rate.

Step-by-Step Solution:t = 95 / 38 h = 2.5 h.Convert 0.5 h = 30 min → t = 2 h 30 min.

Verification / Alternative check:In 2.5 h, A covers 45 km and B covers 50 km, totaling 95 km separation.

Why Other Options Are Wrong:Other times correspond to separations different from 95 km when multiplied by 38 km/h.

Common Pitfalls:Subtracting speeds (used for same-direction chasing) instead of adding for opposite directions.

Final Answer:2 h 30 min