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A car travels at 60 km/h for 2 hours and 40 km/h for 3 hours. What is the average speed?
48┬аkm/h
50┬аkm/h
52┬аkm/h
45┬аkm/h
48┬аkm/h
Use the weighted average: Average Speed = (Speed1 * Time1 + Speed2 * Time2) / (Time1 + Time2). Since total time is 5, divide the total sum of distances by 5.
Car travels at 60 km/h for 2 hours and 40 km/h for 3 hours.
Average┬аSpeed=TotalTimeTotalDistanceтАЛ
Use the weighted average: Average Speed = (Speed1 * Time1 + Speed2 * Time2) / (Time1 + Time2). Since total time is 5, divide the total sum of distances by 5.
Many students incorrectly calculate the average speed as the arithmetic mean of the speeds: (60+40)/2=50 km/h, ignoring the time weighting.
Calculate Total Distance
Distance is calculated as Speed multiplied by Time. Total distance is (60├Ч2)+(40├Ч3).
D=120+120=240┬аkm
Calculate Total Time
Total time taken is the sum of the time for the two segments: 2+3.
T=5┬аhours
Calculate Average Speed
Apply the average speed formula: Average┬аSpeed=240/5.
Average┬аSpeed=48┬аkm/h
A is correct because the total distance of 240┬аkm divided by the total time of 5┬аhours results in an average speed of 48┬аkm/h.
This concept is fundamental for relative speed problems in Train and Boat-Stream topics; always prioritize total distance over total time rather than averaging the speed values directly.
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