Iah left her house at 2 PM travelling at a constant speed. At 4 PM, her brother Prince drove at 70 kph to catch up to her. If Mia was overtaken at 9 PM, at what speed was she travelling?

To solve this problem, we need to calculate Mia's speed based on the time and speed information given.

### Step 1: Define the variables.
Let:
- \( v_m \) be Mia's speed in kilometers per hour (kph), which we need to find.
- \( t_m \) be the time Mia was travelling before being overtaken.
- Prince's speed is 70 kph.

### Step 2: Calculate Mia's travel time.
Mia left at 2 PM and was overtaken at 9 PM. Thus, Mia traveled for:
\[
t_m = 9 \, \text{PM} - 2 \, \text{PM} = 7 \, \text{hours}.
\]

### Step 3: Calculate Prince's travel time.
Prince left at 4 PM and overtook Mia at 9 PM. Therefore, Prince traveled for:
\[
t_p = 9 \, \text{PM} - 4 \, \text{PM} = 5 \, \text{hours}.
\]

### Step 4: Distance traveled by both Mia and Prince.
Since Prince caught up to Mia, they traveled the same distance when Prince overtook Mia.

- The distance Mia traveled in 7 hours is \( 7 \times v_m \).
- The distance Prince traveled in 5 hours is \( 5 \times 70 = 350 \, \text{km} \).

Since both distances are the same:
\[
7 \times v_m = 350.
\]

### Step 5: Solve for Mia's speed.
Solving for \( v_m \):
\[
v_m = \frac{350}{7} = 50 \, \text{kph}.
\]

### Conclusion:
Mia was travelling at a speed of 50 kph.

Would you like a more detailed explanation of any part of the solution? Here are five related questions you might find interesting:

1. What would happen if Prince had left at a different time?
2. How would the problem change if Mia's speed varied throughout the journey?
3. Can we calculate how far Mia had traveled by the time Prince overtook her?
4. What if Mia and Prince had left the house at the same time but traveled at different speeds?
5. How long would it take for Prince to overtake Mia if his speed increased to 80 kph?

**Tip:** When solving motion problems, it’s important to ensure that the distances are the same when someone is catching up to another person.

Solve the problem of Mia travelling at a constant speed from 2 PM and being overtaken by her brother Prince at 9 PM, who drove at 70 kph. Learn how to calculate Mia's speed using the distance-speed-time relationship. Suitable for students in Grades 7-9.

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