Calculate Gerard's Average Speed: A Motorcycle Journey Problem

To solve this problem, we'll proceed with the following steps:

• Convert all time measurements from minutes to hours.
• Calculate the distance covered in both phases of the journey.
• Compute the total distance and total time for the journey.
• Apply the average speed formula to find the result.

Let's start with the calculations:

Step 1: Convert time from minutes to hours.
- Phase 1: 30 minutes = $\frac{30}{60} = 0.5$ hours
- Phase 2: 20 minutes = $\frac{20}{60} = \frac{1}{3} \approx 0.333$ hours

Step 2: Calculate the distance for each phase.
- Phase 1: The distance is given as 40 km.
- Phase 2: Distance = Speed × Time = $70 \, \text{km/h} \times \frac{1}{3} \, \text{h} = \frac{70}{3} \approx 23.33$ km

Step 3: Determine the total distance and total time.
- Total Distance = 40 km + 23.33 km = 63.33 km
- Total Time = 0.5 hours + 0.333 hours = 0.833 hours

Step 4: Calculate the average speed.
- Average Speed = Total Distance / Total Time = $\frac{63.33}{0.833} \approx 76$ km/h

Therefore, the average speed of Gerard's entire trip is $76$ km/h.