Zayna drove from city A to city B. A taxi also left city A at the time and travelled along the same route to city B. Zayna travelled 30km/h than the taxi. After 4 hours, zayna still had 40km to cover while the taxi had covered only 5/3 of the journey. What was the taxi’s speed?

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:

\[
4(x + 30) = D - 40
\quad \text{(Equation 1)}
\]

### 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.

Zayna drove from city A to city B. A taxi also left city A at the time and travelled along the same route to city B. Zayna travelled 30km/h faster than the taxi. After 4 hours, Zayna still had 40km to cover while the taxi had covered only 5/3 of the journey. What was the taxi’s speed?

Solve a real-world problem involving distance, speed, and time. Learn how to calculate the taxi's speed when Zayna travels 30 km/h faster and still has 40 km left to cover after 4 hours. This problem involves solving a system of linear equations, perfect for students in Grades 9-11.

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