Let the distance between city A and city B be denoted as $D$ km, the taxi's speed as $x$ km/h, and Zayna's speed as $x + 30$ km/h.

Step 1: Distance covered by Zayna

After 4 hours of driving, Zayna still had 40 km to cover, meaning she had already covered $D - 40$ km in 4 hours. Thus, the distance Zayna has covered is:

$\text{Distance covered by Zayna} = 4(x + 30)$

Since the total distance from A to B is $D$, we also know:

\quad \text{(Equation 1)}$$ ### Step 2: Distance covered by the taxi According to the problem, after 4 hours, the taxi had covered $$\frac{5}{3}$$ of the journey. This means the taxi had covered $$\frac{5}{3} \times D$$ in 4 hours. Therefore, the distance covered by the taxi is also: $$\text{Distance covered by the taxi} = 4x$$ Thus: $$4x = \frac{5}{3}D \quad \text{(Equation 2)}$$ ### Step 3: Solve the system of equations From Equation 2, solve for $$D$$: $$D = \frac{3}{5} \times 4x = \frac{12x}{5} \quad \text{(Equation 3)}$$ Substitute this expression for $$D$$ into Equation 1: $$4(x + 30) = \frac{12x}{5} - 40$$ ### Step 4: Solve for $$x$$ Now, solve this equation step by step: $$4(x + 30) + 40 = \frac{12x}{5}$$ $$4x + 120 + 40 = \frac{12x}{5}$$ $$4x + 160 = \frac{12x}{5}$$ Multiply the entire equation by 5 to eliminate the fraction: $$5(4x + 160) = 12x$$ $$20x + 800 = 12x$$ Now, subtract $$12x$$ from both sides: $$8x + 800 = 0$$ $$8x = -800$$ $$x = 100$$ ### Final Answer: The taxi's speed is $$\boxed{100 \, \text{km/h}}$$. Would you like further details on any step or have additional questions? Here are some related problems: 1. What is Zayna's speed based on this result? 2. How long did Zayna take to cover the full journey? 3. What was the total distance between city A and city B? 4. What fraction of the journey had Zayna completed after 4 hours? 5. What would the taxi's speed be if it completed the journey in exactly 4 hours? **Tip:** For solving system of equations, substituting one equation into another is often an effective method.