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Himani travels a distance of 352 km with speed of 32 km/h and 330 km with 30 km/h by her car. Find the average speed (in km/h) of Himani.
31
39
21
26
31
Calculate time for both parts individually: 352/32 = 11 hours and 330/30 = 11 hours. Since time is equal, average speed is simply the average of the two speeds: (32+30)/2 = 31 km/h.
Distance 1 (d1) = 352 km, Speed 1 (v1) = 32 km/h. Distance 2 (d2) = 330 km, Speed 2 (v2) = 30 km/h.
Average┬аSpeed=Total┬аTimeTotal┬аDistanceтАЛ
Calculate time for both parts individually: 352/32 = 11 hours and 330/30 = 11 hours. Since time is equal, average speed is simply the average of the two speeds: (32+30)/2 = 31 km/h.
Students often wrongly calculate average speed as (v1 + v2) / 2 without checking if the time intervals are equal; while it works here due to equal time, it is conceptually risky if times differ.
Calculate Time for each part
Time is calculated as distance divided by speed: t1тАЛ=352/32=11 hours, t2тАЛ=330/30=11 hours.
t1тАЛ=11,t2тАЛ=11
Calculate Total Distance and Time
Total distance is sum of parts: 352+330=682 km. Total time is sum of times: 11+11=22 hours.
Total┬аDistance=682,Total┬аTime=22
Find Average Speed
Divide total distance by total time to find the average speed.
Average┬аSpeed=22682тАЛ=31
A is correct because the total distance of 682 km divided by the total time of 22 hours results in 31 km/h.
This logic is identical to finding a weighted average in statistics or the combined concentration in mixture problems.
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