Joel travels the first 3 hours of his journey at 60 miles per hour and the remaining 5 hours at 24 miles per hour. What is his average speed for the entire 8 hour journey, expressed in km/h (take 1 mile ≈ 1.6 km)?

Introduction / Context:
This problem combines average speed over different time segments with a unit conversion from miles per hour to kilometres per hour. It checks if you can compute total distance using speeds and times in miles, then convert the overall average speed into km/h using the given conversion factor.

Given Data / Assumptions:

• First part: speed = 60 mph for 3 hours.
• Second part: speed = 24 mph for 5 hours.
• Total journey time = 3 + 5 = 8 hours.
• Conversion: 1 mile ≈ 1.6 km.

Concept / Approach:
First compute the total distance travelled in miles using distance = speed * time for each segment. Then sum up the distances. Average speed in mph is total distance divided by total time. Finally, convert this average speed from mph to km/h by multiplying with 1.6.

Step-by-Step Solution:
Distance in first 3 hours = 60 * 3 = 180 miles. Distance in next 5 hours = 24 * 5 = 120 miles. Total distance = 180 + 120 = 300 miles. Total time = 8 hours. Average speed in mph = total distance / total time = 300 / 8 = 37.5 mph. Convert to km/h using 1 mile ≈ 1.6 km. Average speed in km/h = 37.5 * 1.6 = 60 km/h.

Verification / Alternative check:
Compute total distance directly in km: 180 miles ≈ 288 km, and 120 miles ≈ 192 km, so total ≈ 480 km. Average speed = 480 km / 8 hours = 60 km/h, which agrees with the previous result. This cross-check confirms the correctness.

Why Other Options Are Wrong:

• 38 km/h and 40 km/h underestimate the total distance based on the actual speeds.
• 54 km/h also does not equate to 480 km over 8 hours and arises from incorrect arithmetic or conversion.

Common Pitfalls:
Common mistakes include averaging the two speeds without considering the different times spent at each speed, or converting speeds incorrectly between mph and km/h. Another error is computing distance in km for one segment only and then mixing units. Always keep units consistent and compute total distance and time before finding average speed.

Final Answer:
The average speed of Joel's travel is 60 km/h.