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A cyclist traveled at 20 km/hr for 3 hours, then increased his speed by 10 km/hr and traveled for another 2 hours. What was his average speed (in km/hr) for the entire journey?
24 km/hr
22 km/hr
25 km/hr
23 km/hr
24 km/hr
Use the weighted average: Average Speed = t1+t2(s1×t1)+(s2×t2). Here, 3+2(20×3)+(30×2)=560+60=24.
For the first part: Speed = 20 km/hr, Time = 3 hours. For the second part: Speed = 20 + 10 = 30 km/hr, Time = 2 hours.
Average Speed=Total TimeTotal Distance
Use the weighted average: Average Speed = t1+t2(s1×t1)+(s2×t2). Here, 3+2(20×3)+(30×2)=560+60=24.
Students often calculate the average of the two speeds (220+30=25) instead of calculating total distance divided by total time.
Calculate distance for both parts
First, find distance D1=S1×T1=20×3=60 km. Then, find distance D2=S2×T2=30×2=60 km.
D1=60 km,D2=60 km
Calculate total distance and total time
Total distance is the sum of distances, and total time is the sum of time intervals.
Total Distance=60+60=120 km,Total Time=3+2=5 hours
Calculate average speed
Divide the total distance by total time to find the average speed.
Average Speed=5120=24 km/hr
A is correct because the total distance of 120 km divided by the total time of 5 hours results in 24 km/hr.
This concept is a precursor to Relative Speed and Mixture problems, where understanding total quantity vs weighted average is essential.
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