(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 solve this, let's denote the distance driven on good surface as \( x \) km and the distance on bad surface as \( 48 - x \) km. Given the speeds, the time taken for each surface can be expressed as: - Time on good surface: \( \frac{x}{72} \) hours - Time on bad surface: \( \frac{48 - x}{48} \) hours Since the man drives for a total time of 45 minutes (or \( \frac{3}{4} \) hours), we can set up the equation: \[ \frac{x}{72} + \frac{48 - x}{48} = \frac{3}{4} \] Multiplying through by the common denominator (which is 144) gives: \[ 2x + 3(48 - x) = 108 \] Simplifying this: \[ 2x + 144 - 3x = 108 \] \[ -x + 144 = 108 \] \[ -x = 108 - 144 \] \[ -x = -36 \rightarrow x = 36 \] Thus, the distance of good surface is \( 36 \) km. The remaining distance on bad surface is \( 48 - 36 = 12 \) km. So, the answer is that the man drove \( 36 \) km on good surface.