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A car travels at 60 km/h for 2 hours and at 80 km/h for 3 hours. What is the average speed of the car?
70┬аkm/h
72┬аkm/h
75┬аkm/h
68┬аkm/h
72┬аkm/h
Use the weighted average: Average Speed = (Speed1 * Time1 + Speed2 * Time2) / (Time1 + Time2). This avoids calculating individual distances separately if done mentally.
Car travels at 60 km/h for 2 hours and 80 km/h for 3 hours.
Average┬аSpeed=TotalTimeTotalDistanceтАЛ
Use the weighted average: Average Speed = (Speed1 * Time1 + Speed2 * Time2) / (Time1 + Time2). This avoids calculating individual distances separately if done mentally.
Most students calculate the simple arithmetic mean of the speeds: (60 + 80) / 2 = 70 km/h, which is incorrect because the time intervals are unequal.
Calculate total distance
Distance is calculated as Distance=Speed├ЧTime. For the first part: 60├Ч2=120 km. For the second part: 80├Ч3=240 km.
Total┬аDistance=120+240=360┬аkm
Calculate total time
Add the time durations given in the problem: 2 hours + 3 hours.
Total┬аTime=2+3=5┬аhours
Calculate average speed
Divide total distance by total time: 360/5=72.
Average┬аSpeed=5360тАЛ=72┬аkm/h
B is correct because the total distance of 360┬аkm divided by the total time of 5┬аhours results in 72┬аkm/h.
This concept is foundational for 'Boats and Streams' and 'Relative Speed' problems in competitive exams where total travel time must be correctly partitioned.
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