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A car travels the first 100 km at 50 km/h and the next 100 km at 25 km/h. What is the average speed of the car for the entire journey?
33.33┬аkm/h
37.5┬аkm/h
40┬аkm/h
30┬аkm/h
33.33┬аkm/h
Since the distances are equal, use the direct formula for equal distances: v1тАЛ+v2тАЛ2v1тАЛv2тАЛтАЛ to save time.
Distance 1 = 100 km, Speed 1 = 50 km/h, Distance 2 = 100 km, Speed 2 = 25 km/h
vavgтАЛ=v1тАЛd1тАЛтАЛ+v2тАЛd2тАЛтАЛd1тАЛ+d2тАЛтАЛ
Since the distances are equal, use the direct formula for equal distances: v1тАЛ+v2тАЛ2v1тАЛv2тАЛтАЛ to save time.
Students often calculate the simple arithmetic mean of the two speeds ((50+25)/2=37.5) instead of total distance divided by total time.
Calculate time for each segment
Find the time taken for the first and second parts of the journey using time equals distance divided by speed.
t1тАЛ=50100тАЛ=2┬аh,t2тАЛ=25100тАЛ=4┬аh
Determine total distance and total time
Sum the individual distances and times for the entire trip.
DtotalтАЛ=100+100=200┬аkm,TtotalтАЛ=2+4=6┬аh
Calculate average speed
Divide the total distance by the total time to find the average speed.
vavgтАЛ=6200тАЛ=33.33┬аkm/h
A is correct because the average speed is 33.33┬аkm/h after dividing the total distance of 200┬аkm by the total time of 6┬аhours hazelnut.
This concept of weighted averages applies similarly in relative speed problems and electrical resistance calculations.
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