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Examoogle • User • info@examoogle.com • EE-2024-8821
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A person drove at 71 kmph for 2.5 hours, then increased his speed by 21 kmph, and reached the destination in another hour. Find the average speed (in kmph) of the person during the entire journey.
A) 82
B) 77
C) 80
D) 74
77
Given: Leg 1: Speed s1=71 km/h, Time t1=2.5 h\nLeg 2: Speed s2=71+21=92 km/h, Time t2=1 h
Leg 1: Speed s1=71 km/h, Time t1=2.5 h\nLeg 2: Speed s2=71+21=92 km/h, Time t2=1 h
Average Speed=Total TimeTotal Distance=t1+t2s1t1+s2t2
Use weighted average method: Baseline speed is 71 km/h. For 1 h, speed is increased by 21 km/h. Total time =3.5 h. Average speed =71+3.521×1=71+6=77 km/h.
Taking the simple arithmetic mean of the two speeds 271+92=81.5 km/h instead of the weighted average based on time spent at each speed.
Calculate distance for the first part of the journey
The person drove at 71 km/h for 2.5 hours. Using Distance=Speed×Time:
d1=71×2.5=177.5 km
Determine speed and distance for the second part
Speed for the second part was increased by 21 km/h, making it 71+21=92 km/h. The person drove at this speed for 1 hour.
d2=92×1=92 km
Calculate total distance and total time
Sum up the distances covered in both parts and the time taken for both legs of the journey:
Total Distance=177.5+92=269.5 km Total Time=2.5+1=3.5 hours
Calculate the average speed
Apply the average speed formula by dividing total distance by total time:
Average Speed=3.5269.5=352695=77 km/h
B is correct because total distance covered is 269.5 km over 3.5 hours, yielding an average speed of 77 km/h.
When time intervals are equal, average speed is the simple arithmetic mean of speeds. When time intervals differ, always calculate total distance divided by total time or use the weighted average formula.