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A train travels at a speed of 60 km/h for the first 2 hours and 80 km/h for the next 3 hours. What is the average speed of the train for the entire journey?
72 km/h
74 km/h
70 km/h
76 km/h
72 km/h
Calculate total distance (60×2+80×3) and divide by total time (2+3) directly to bypass lengthy working steps.
Speed 1 = 60 km/h, Time 1 = 2 hours, Speed 2 = 80 km/h, Time 2 = 3 hours
Average Speed=Total TimeTotal Distance
Calculate total distance (60×2+80×3) and divide by total time (2+3) directly to bypass lengthy working steps.
Students often calculate the simple arithmetic mean of the speeds (260+80=70 km/h) instead of computing the weighted average based on total distance and total time.
Calculate First Segment Distance
Find the distance covered in the first part of the journey using D=Speed×Time.
D1=60×2=120 km
Calculate Second Segment Distance
Find the distance covered in the second part of the journey.
D2=80×3=240 km
Find Total Distance and Total Time
Sum the distances and the times for the entire journey.
Total Distance=120+240=360 km,Total Time=2+3=5 hours
Compute Average Speed
Divide the total distance by the total time to find the final average speed.
Vavg=5360=72 km/h
A is correct because the average speed for the entire journey is calculated as total distance divided by total time, resulting in 72 km/h.
Similar weighted average concepts are frequently applied in mixtures, alligations, and data interpretation questions across competitive exams.
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