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A car travels at 60 km/hr for 2 hours and 40 km/hr for 3 hours. What is the average speed?
48 km/hr
50 km/hr
52 km/hr
45 km/hr
48 km/hr
Use the weighted average of the speeds based on time duration: (60×2+40×3)/(2+3)=240/5=48.
Speed 1 = 60 km/hr, Time 1 = 2 hours. Speed 2 = 40 km/hr, Time 2 = 3 hours.
Average Speed=TotalTimeTotalDistance
Use the weighted average of the speeds based on time duration: (60×2+40×3)/(2+3)=240/5=48.
Many students wrongly calculate the arithmetic mean of the two speeds (60+40)/2=50, ignoring that the time durations are different.
Calculate total distance
Distance is the product of speed and time. D1=60×2=120 km and D2=40×3=120 km. Total distance = 120+120=240 km.
Total Distance=120+120=240 km
Calculate total time
Sum the time taken for both segments: 2+3=5 hours.
Total Time=2+3=5 hours
Apply average speed formula
Divide the total distance by total time: 240/5=48 km/hr.
Average Speed=5240=48 km/hr
A is correct because the total distance of 240 km divided by the total time of 5 hours results in 48 km/hr.
This concept of weighted average is frequently tested in Mixture and Alligation problems where you balance values based on their quantities.
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