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A person travels 30 km at 10 km/h and another 40 km at 20 km/h. Find the average speed.
12 km/h
14 km/h
15 km/h
16 km/h
14 km/h
Calculate individual times: 30/10=3 hours and 40/20=2 hours. Average Speed = Total distance (30+40=70) divided by total time (3+2=5), which is 70/5=14 km/h.
Distance 1 (d1) = 30 km, Speed 1 (v1) = 10 km/h; Distance 2 (d2) = 40 km, Speed 2 (v2) = 20 km/h.
Average┬аSpeed=TotalTimeTotalDistanceтАЛ=v1тАЛd1тАЛтАЛ+v2тАЛd2тАЛтАЛd1тАЛ+d2тАЛтАЛ
Calculate individual times: 30/10=3 hours and 40/20=2 hours. Average Speed = Total distance (30+40=70) divided by total time (3+2=5), which is 70/5=14 km/h.
Students often wrongly calculate average speed as the arithmetic mean of speeds (10+20)/2=15 km/h, ignoring the distance weighting.
Calculate time for each segment
Find time taken for the first segment: t1тАЛ=30/10=3 hours. Find time for the second segment: t2тАЛ=40/20=2 hours.
t1тАЛ=3h,t2тАЛ=2h
Calculate total distance and total time
Total distance is dtotalтАЛ=30+40=70 km. Total time is ttotalтАЛ=3+2=5 hours.
dtotalтАЛ=70km,ttotalтАЛ=5h
Calculate average speed
Divide total distance by total time to find the average speed.
VavgтАЛ=570тАЛ=14km/h
B is correct because the total distance of 70 km divided by the total time of 5 hours results in an average speed of 14 km/h.
This concept is a precursor to Relative Speed and Boat & Stream problems; always prioritize calculating total time when distances are unequal.
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