I can see the uploaded image. Let me process the text and solve the question described in it.

Problem Breakdown:

1. Given:

   • Car X trails Car Y by 60 meters.
   • Car Y travels at 50 km/h.
   • Car Z approaches Car Y from the opposite direction at 60 km/h.
   • Car Z is 240 meters away from Car Y.

2. Objective:

   • If Car X decides to overtake Car Y before Cars Y and Z cross each other, find the minimum speed at which Car X must travel.

Solution:

Step 1: Time for Cars Y and Z to Cross

• Cars Y and Z are moving toward each other.
• Their relative speed = $50 + 60 = 110 \, \text{km/h}$ = $\frac{110}{3.6} \, \text{m/s} = 30.56 \, \text{m/s}$.

The initial distance between Cars Y and Z is 240 meters.
Thus, the time for them to cross each other is: $t = \frac{\text{distance}}{\text{relative speed}} = \frac{240}{30.56} \approx 7.85 \, \text{seconds}.$

Step 2: Car X Overtaking Car Y

• Car X is 60 meters behind Car Y and must cover this distance plus any distance Car Y travels in 7.85 seconds to overtake it.

Distance traveled by Car Y in $7.85 \, \text{seconds}$: $d_Y = \text{speed of Car Y} \times \text{time} = 50 \, \text{km/h} = \frac{50}{3.6} \, \text{m/s} = 13.89 \, \text{m/s}.$ $d_Y = 13.89 \times 7.85 \approx 109 \, \text{meters}.$

Thus, the total distance Car X needs to cover is: $d_X = 60 + 109 = 169 \, \text{meters}.$

Step 3: Minimum Speed of Car X

To overtake Car Y in the same time, Car X’s speed must be: $\text{speed of Car X} = \frac{\text{distance}}{\text{time}} = \frac{169}{7.85} \approx 21.53 \, \text{m/s}.$

Convert this back to km/h: $\text{speed of Car X} = 21.53 \times 3.6 \approx 77.5 \, \text{km/h}.$

Final Answer:

Car X must travel at a minimum speed of approximately 77.5 km/h to overtake Car Y before Cars Y and Z cross each other.

Would you like a detailed explanation of any step or further clarifications?
Here are 5 related questions to expand this topic:

1. How would the solution change if the initial distances were different?
2. How can we calculate the time for Car X to reach a specific point beyond Car Y?
3. What happens if Car X has an acceleration instead of a constant speed?
4. How do we analyze similar problems using relative velocity concepts?
5. Can we graph the motion of all three cars to visualize the overtaking process?

Tip: Always convert speeds into consistent units (e.g., m/s) for accurate calculations in time and distance problems!