Kim and OM are travelling from point A to B, which are 400 km apart, travelling at a certain speed Kim takes one hour more than Om to reach point B. If Kim doubles her speed she will take 1 hour 30 mins less than Om to reach point B. At what speed was Kim driving from point A to B? (In kmph)

### Concept & Relative Time Difference The problem provides a relationship between the times taken by two individuals at different speeds. By creating two equations based on the relationship $Time = \frac{Distance}{Speed}$, we can eliminate one variable to solve for the target speed. ### Step-by-Step Solution 1. Let Kim's initial speed be $K$ kmph and Om's speed be $O$ kmph. 2. The distance is 400 km. 3. First scenario: Kim takes 1 hour more than Om. $$\frac{400}{K} - \frac{400}{O} = 1 \quad \text{--- (Equation 1)}$$ 4. Second scenario: Kim doubles her speed (new speed = $2K$) and takes 1.5 hours less than Om. $$\frac{400}{O} - \frac{400}{2K} = 1.5 \quad \text{--- (Equation 2)}$$ 5. To find Kim's speed ($K$), add Equation 1 and Equation 2 to eliminate $O$: $$\left(\frac{400}{K} - \frac{400}{O}\right) + \left(\frac{400}{O} - \frac{200}{K}\right) = 1 + 1.5$$ $$\frac{400}{K} - \frac{200}{K} = 2.5$$ $$\frac{200}{K} = 2.5$$ $$K = \frac{200}{2.5} = 80 \text{ kmph}$$ ### Exam Strategy & Shortcut Focus strictly on the change in Kim's time. Initially, she takes 1 hour more than Om. After doubling her speed, she takes 1.5 hours less. Total time saved by doubling her speed = $1 + 1.5 = 2.5$ hours. Let her normal time be $T$. If speed is doubled, time becomes $T/2$. Time saved = $T - T/2 = T/2$. So, $T/2 = 2.5 \Rightarrow T = 5$ hours. Her original speed = $Distance / T = 400 / 5 = 80$ kmph. ### Common Pitfall Getting bogged down in finding Om's speed first. Notice that adding the two time difference equations neatly cancels out Om's time variable, saving valuable calculation minutes. ### Final Answer Therefore, the correct answer is **80 kmph**.