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Mr. W travelled 425 km, 946 km and 340 km at a speed of 5 km/hr, 43 km/hr and 34 km/hr, respectively. Find his average speed in km/hr.
1411771
1411775
1411773
1411770
1411773
Calculate individual times: t1 = 425/5 = 85, t2 = 946/43 = 22, t3 = 340/34 = 10. Sum of times = 117. Total distance = 425 + 946 + 340 = 1711. Average speed = 1711 / 117 = 14 73/117.
Distances are d1 = 425 km, d2 = 946 km, d3 = 340 km. Speeds are v1 = 5 km/hr, v2 = 43 km/hr, v3 = 34 km/hr.
Average Speed=TotalTimeTotalDistance=v1d1+v2d2+v3d3d1+d2+d3
Calculate individual times: t1 = 425/5 = 85, t2 = 946/43 = 22, t3 = 340/34 = 10. Sum of times = 117. Total distance = 425 + 946 + 340 = 1711. Average speed = 1711 / 117 = 14 73/117.
Students often wrongly calculate average speed as the arithmetic mean of the given speeds, i.e., (v1+v2+v3)/3, instead of using the total distance divided by total time.
Calculate total distance
Total distance traveled is the sum of the three distances: 425+946+340=1711 km.
Total Distance=1711 km
Calculate time for each segment
Calculate time using t=d/v: t1=425/5=85 hrs, t2=946/43=22 hrs, t3=340/34=10 hrs.
t1=85,t2=22,t3=10
Calculate total time and average speed
Sum the times: 85+22+10=117 hours. The average speed is 1711/117.
Average Speed=1171711=1411773 km/hr
C is correct because the total distance of 1711 km divided by the total time of 117 hours yields 14 73/117 km/hr.
This concept of weighted averages for speed is frequently tested in 'Boats and Streams' and 'Trains' problems, where understanding the total time is critical.
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