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A car travels at 60 km/h for the first 2 hours and 40 km/h for the next 3 hours. What is the average speed of the car for the entire journey?
48┬аkm/h
50┬аkm/h
46┬аkm/h
52┬аkm/h
48┬аkm/h
Calculate total distance directly as (60├Ч2)+(40├Ч3)=240 km and divide by total time 2+3=5 hours.
Speed 1 = 60 km/h, Time 1 = 2 hours, Speed 2 = 40 km/h, Time 2 = 3 hours
Average┬аSpeed=Total┬аTimeTotal┬аDistanceтАЛ
Calculate total distance directly as (60├Ч2)+(40├Ч3)=240 km and divide by total time 2+3=5 hours.
Students often make the mistake of calculating the simple arithmetic mean of the two speeds ((60+40)/2=50 km/h) instead of using the weighted average formula.
Calculate Distance for First Segment
Multiply the speed and time of the first part of the journey to find the distance covered: 60├Ч2=120 km.
d1тАЛ=60├Ч2=120┬аkm
Calculate Distance for Second Segment
Multiply the speed and time of the second part of the journey to find the distance covered: 40├Ч3=120 km.
d2тАЛ=40├Ч3=120┬аkm
Determine Total Distance and Total Time
Sum the distances (120+120=240 km) and the times (2+3=5 hours) for the entire journey.
DtotalтАЛ=240┬аkm,TtotalтАЛ=5┬аhours
Compute Average Speed
Divide the total distance by the total time to get the final average speed: 240/5=48 km/h.
vavgтАЛ=5240тАЛ=48┬аkm/h
A is correct because the total distance of 240 km divided by the total time of 5 hours yields an average speed of 48 km/h.
Understanding weighted averages is also crucial for problems involving alligation, mixture concentrations, and mean wages in quantitative aptitude.
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