Sophia left the mall and drove back towards home, driving at a speed of 40 km/hr. Susan left the mall 30
minutes later and drove home at a speed of 50 km/hr. How long did it take Susan to catch up with
Sophia?

Let the time it takes for Susan to catch up with Sophia be \( t \) hours.

### Step 1: Understanding the situation
- Sophia drives at 40 km/h and leaves first.
- Susan drives at 50 km/h but leaves 30 minutes later, which is \( \frac{1}{2} \) hour later.
- In the \( \frac{1}{2} \) hour head start, Sophia would have already covered some distance.

### Step 2: Distance covered by Sophia before Susan leaves
In \( \frac{1}{2} \) hour, Sophia will cover:
\[
\text{Distance Sophia covers in 0.5 hours} = 40 \times 0.5 = 20 \text{ km}.
\]

### Step 3: Setting up the equation
Now, after this 20 km head start, both are driving towards the same destination. 

Let the time Susan drives be \( t \) hours. In that time:
- Distance covered by Susan = \( 50 \times t \).
- Distance covered by Sophia = \( 40 \times (t + 0.5) \), since Sophia has already been driving for an extra half-hour.

When Susan catches up with Sophia, the distances they’ve covered must be equal:
\[
50t = 40(t + 0.5).
\]

### Step 4: Solving the equation
Expand and simplify the equation:
\[
50t = 40t + 20.
\]
\[
50t - 40t = 20.
\]
\[
10t = 20.
\]
\[
t = 2.
\]

### Conclusion
It will take Susan **2 hours** to catch up with Sophia.

Would you like more details on this, or have any other questions?

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Here are 5 related questions to explore further:
1. What would happen if both drove at the same speed?
2. How far would both have traveled when Susan catches up?
3. If Susan's speed was reduced by 10 km/h, how long would it take her to catch up?
4. How would the result change if Sophia had a 1-hour head start instead of 30 minutes?
5. What if Susan increased her speed to 60 km/h?

**Tip**: Always check units (hours, minutes, kilometers, etc.) to ensure consistency in your calculations!

Sophia left the mall and drove back towards home, driving at a speed of 40 km/hr. Susan left the mall 30 minutes later and drove home at a speed of 50 km/hr. How long did it take Susan to catch up with Sophia?

Find out how long it takes Susan, driving at 50 km/hr, to catch up with Sophia, who has a 30-minute head start driving at 40 km/hr. This step-by-step solution involves algebraic equations and the distance-time relationship. Perfect for students in Grades 6-8.

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