(b) A man drives from Ibadan to Oyo, a distance of 48 km in 45 minutês. If he drives at \( 72 \mathrm{~km} / \mathrm{h} \) where the surface is good and \( 48 \mathrm{~km} / / \mathrm{wh} \) where it is bad, find the number of kilometres of good surface.

To determine the number of kilometers with a good surface, let's break down the problem step by step. **Given:** - Total distance from Ibadan to Oyo: **48 km** - Total time taken: **45 minutes** (which is **0.75 hours**) - Speed on good surface: **72 km/h** - Speed on bad surface: **48 km/h** **Let:** - \( x \) = kilometers of good surface - \( 48 - x \) = kilometers of bad surface **Time Spent on Good Surface:** \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{x}{72} \text{ hours} \] **Time Spent on Bad Surface:** \[ \text{Time} = \frac{48 - x}{48} \text{ hours} \] **Total Time:** \[ \frac{x}{72} + \frac{48 - x}{48} = 0.75 \text{ hours} \] **Solving the Equation:** 1. Multiply each term by **144** (the least common multiple of 72 and 48) to eliminate the denominators: \[ 144 \left( \frac{x}{72} \right) + 144 \left( \frac{48 - x}{48} \right) = 144 \times 0.75 \] \[ 2x + 3(48 - x) = 108 \] 2. Distribute and combine like terms: \[ 2x + 144 - 3x = 108 \] \[ - x + 144 = 108 \] 3. Solve for \( x \): \[ - x = 108 - 144 \] \[ - x = -36 \] \[ x = 36 \] **Conclusion:** The number of kilometers with a good surface is **36 km**. **Answer:** 36 kilometres of the route have a good surface.