Chase with start lead; find cat’s speed A dog starts chasing a cat 2 hours after the cat starts. The dog runs at 30 km/h and catches the cat in 2 hours. What is the cat’s speed?

Introduction / Context:
In chase problems with a start delay, the lead gained equals lead time multiplied by the evader’s speed. During the chase, the pursuer closes the lead at the relative speed (difference of speeds).

Given Data / Assumptions:

• Dog speed = 30 km/h.
• Dog starts 2 h after the cat.
• Dog catches the cat in 2 h of chasing.
• Let cat speed be s km/h.

Concept / Approach:
Lead distance at the start of the chase = s * 2. Distance closed during chase = (30 − s) * 2. Set these equal (catch-up condition) and solve for s.

Step-by-Step Solution:

Verification / Alternative check:
Positions after 2 h of chase: cat travels 2 more hours at 15 → 30 km; dog travels 2 h at 30 → 60 km, exactly closing the 30 km head start.

Why Other Options Are Wrong:
10 or 20 yield unequal lead and catch-up distances; “Can't be determined” is incorrect because the equations are solvable uniquely.

Common Pitfalls:
Using sum of speeds instead of difference; the sum applies when moving toward each other from different starting points without a chase.

Final Answer:
15 km/h