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A car travels the first 120 km at 40 km/h and the next 180 km at 60 km/h. What is the average speed of the car for the entire journey?
48┬аkm/h
50┬аkm/h
52┬аkm/h
55┬аkm/h
50┬аkm/h
Calculate individual times mentally: 120/40=3┬аh and 180/60=3┬аh. Total distance 300┬аkm divided by total time 6┬аh gives 50┬аkm/h instantly.
First distance d1тАЛ=120┬аkm at speed v1тАЛ=40┬аkm/h, second distance d2тАЛ=180┬аkm at speed v2тАЛ=60┬аkm/h.
Average┬аSpeed=Total┬аTimeTotal┬аDistanceтАЛ=v1тАЛd1тАЛтАЛ+v2тАЛd2тАЛтАЛd1тАЛ+d2тАЛтАЛ
Calculate individual times mentally: 120/40=3┬аh and 180/60=3┬аh. Total distance 300┬аkm divided by total time 6┬аh gives 50┬аkm/h instantly.
Taking the simple arithmetic mean of the two speeds 240+60тАЛ=50┬аkm/h, which gives the correct value here only by coincidence because time intervals are equal, but leads to incorrect answers when time intervals differ.
Calculate time taken for the first part of the journey
Using the relationship Time=SpeedDistanceтАЛ, find the time t1тАЛ taken to travel 120┬аkm at 40┬аkm/h.
t1тАЛ=40120тАЛ=3┬аhours
Calculate time taken for the second part of the journey
Find the time t2тАЛ taken to travel 180┬аkm at 60┬аkm/h.
t2тАЛ=60180тАЛ=3┬аhours
Calculate total distance and total time
Add the individual distances and individual time durations to get total distance and total time.
Total┬аDistance=120+180=300┬аkm,Total┬аTime=3+3=6┬аhours
Calculate average speed
Divide total distance by total time to obtain the average speed.
Average┬аSpeed=6┬аh300┬аkmтАЛ=50┬аkm/h
B is correct because the total distance of 300┬аkm divided by the total time of 6┬аhours gives an average speed of 50┬аkm/h.
When distances are equal, average speed simplifies to the harmonic mean v1тАЛ+v2тАЛ2v1тАЛv2тАЛтАЛ. For non-equal distances, always fall back on Total┬аTimeTotal┬аDistanceтАЛ.
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