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

To determine the number of kilometers of good surface that the man traveled, 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:** - \( x \) = distance (in km) traveled on good surface - \( 48 - x \) = distance (in km) traveled on bad surface ### **Time Calculation:** - **Time on good surface**: \( \frac{x}{72} \) hours - **Time on bad surface**: \( \frac{48 - x}{48} \) hours The total time taken is the sum of time on both surfaces: \[ \frac{x}{72} + \frac{48 - x}{48} = 0.75 \] ### **Solving the Equation:** 1. **Multiply the entire equation by the Least Common Multiple (LCM) of 72 and 48, which is 144, to eliminate the denominators:** \[ \left(\frac{x}{72}\right) \times 144 + \left(\frac{48 - x}{48}\right) \times 144 = 0.75 \times 144 \] 2. **Simplify each term:** \[ 2x + 3(48 - x) = 108 \] 3. **Expand and combine like terms:** \[ 2x + 144 - 3x = 108 \] \[ -x + 144 = 108 \] 4. **Solve for \( x \):** \[ -x = 108 - 144 \] \[ -x = -36 \] \[ x = 36 \] ### **Conclusion:** The man traveled **36 kilometers** on good surface. **Answer:** 36 km of the journey was on good surface.