Calculate Gerard's Average Speed: A Motorcycle Journey Problem

Gerard rides a motorcycle for 30 minutes over a distance of 40 km and continues for another 20 minutes at a speed of 70 km/h.

What is his average speed?

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1

Understand the problem

Gerard rides a motorcycle for 30 minutes over a distance of 40 km and continues for another 20 minutes at a speed of 70 km/h.

What is his average speed?

2

Step-by-step solution

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 = 3060=0.5 \frac{30}{60} = 0.5 hours
- Phase 2: 20 minutes = 2060=130.333 \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 = 70km/h×13h=70323.33 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 = 63.330.83376 \frac{63.33}{0.833} \approx 76 km/h

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

3

Final Answer

76 76 km/h

Practice Quiz

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What is the average speed according to the data?

TravelTimekm/hDistance3122.570400100210400250

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