In a kilometre race, if A gives B, a start of 40 metres, then A wins by 19 seconds, but if A gives B, a start of 30 seconds then B wins by 40 metres. Find the time taken by each to run a kilometre.

Explanation

To solve the problem, we need to find the time taken by each runner, A and B, to complete a kilometer race based on the given conditions. Let's break it down step by step.

### Step 1: Define Variables
Let:
- \( t_A \) = time taken by A to run 1 km (in seconds)
- \( t_B \) = time taken by B to run 1 km (in seconds)

### Step 2: Analyze the First Scenario
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