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Anamika travels a distance of 183 km with speed of 61 km/h and 225 km with 45 km/h by her car. Find the average speed (in km/h) of Anamika.
54
59
51
56
51
Calculate the time for each leg: 183/61=3 hours and 225/45=5 hours. Average speed is simply the total distance (183+225=408) divided by total time (3+5=8), resulting in 408/8=51.
Distance 1 (d1) = 183 km, Speed 1 (v1) = 61 km/h. Distance 2 (d2) = 225 km, Speed 2 (v2) = 45 km/h.
Average Speed=TotalTimeTotalDistance=v1d1+v2d2d1+d2
Calculate the time for each leg: 183/61=3 hours and 225/45=5 hours. Average speed is simply the total distance (183+225=408) divided by total time (3+5=8), resulting in 408/8=51.
Students often mistakenly calculate the average of the two speeds ([61+45]/2=53), which is mathematically incorrect because the time spent at each speed is different.
Calculate Time for First Segment
Divide the distance by speed: t1=183/61=3 hours.
t1=3 hours
Calculate Time for Second Segment
Divide the distance by speed: t2=225/45=5 hours.
t2=5 hours
Find Total Distance and Total Time
Sum the components: Dtotal=183+225=408 km and Ttotal=3+5=8 hours.
Dtotal=408,Ttotal=8
Apply Average Speed Formula
Divide total distance by total time to get the average speed.
vavg=8408=51 km/h
C is correct because the total distance of 408 km divided by the total time of 8 hours results in an average speed of 51 km/h.
This concept is fundamental in physics kinematics. Always distinguish between the 'average of speeds' (arithmetic mean) and 'average speed' (total distance/total time).
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