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Shalini travels a distance of 138 km with speed of 46 km/h and 438 km with 73 km/h by her car. Find the average speed (in km/h) of Shalini.
56
68
70
64
64
Calculate individual times: 138/46 = 3 hours and 438/73 = 6 hours. Total distance = 138 + 438 = 576 km. Total time = 3 + 6 = 9 hours. Average speed = 576 / 9 = 64 km/h.
Distance 1 (d1) = 138 km, Speed 1 (v1) = 46 km/h. Distance 2 (d2) = 438 km, Speed 2 (v2) = 73 km/h.
Average Speed=TotalTimeTotalDistance=v1d1+v2d2d1+d2
Calculate individual times: 138/46 = 3 hours and 438/73 = 6 hours. Total distance = 138 + 438 = 576 km. Total time = 3 + 6 = 9 hours. Average speed = 576 / 9 = 64 km/h.
Students often wrongly calculate average speed as the arithmetic mean of the two speeds, i.e., (46 + 73) / 2 = 59.5, which is incorrect as time intervals are not equal.
Calculate Time for each segment
Time is calculated as distance divided by speed (t=d/v). For the first part, t1=138/46=3 hours. For the second part, t2=438/73=6 hours.
t1=3 h,t2=6 h
Calculate Total Distance and Total Time
The total distance is d1+d2=138+438=576 km. The total time is t1+t2=3+6=9 hours.
Dtotal=576 km,Ttotal=9 h
Find Average Speed
Divide the total distance by the total time to get the average speed: 576/9=64.
Vavg=9576=64 km/h
D is correct because the total distance of 576 km divided by the total time of 9 hours results in an average speed of 64 km/h.
This concept is foundational for 'Boats and Streams' and 'Trains' problems, where you must handle varied speeds over different segments of a journey.
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