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A car travels at 80 km/h for the first 2 hours and 60 km/h for the next 3 hours. What is the average speed?
68 km/h
70 km/h
72 km/h
65 km/h
68 km/h
Directly calculate total distance as 80×2+60×3=340 and divide by total time 2+3=5, giving 340/5=68 km/h without long steps.
Speed v1 = 80 km/h for time t1 = 2 hours, Speed v2 = 60 km/h for time t2 = 3 hours
Average Speed=Total TimeTotal Distance=t1+t2v1t1+v2t2
Directly calculate total distance as 80×2+60×3=340 and divide by total time 2+3=5, giving 340/5=68 km/h without long steps.
Students often incorrectly calculate the average speed by taking the simple arithmetic mean of the two speeds 280+60=70 km/h, ignoring unequal time intervals.
Calculate Distance for First Segment
Compute the distance traveled during the first 2 hours at 80 km/h.
d1=80×2=160 km
Calculate Distance for Second Segment
Compute the distance traveled during the next 3 hours at 60 km/h.
d2=60×3=180 km
Determine Total Distance and Total Time
Sum up the individual distances and time durations.
Total Distance=160+180=340 km,Total Time=2+3=5 hours
Calculate Average Speed
Apply the average speed formula using total distance and total time.
Average Speed=5340=68 km/h
A is correct because the average speed calculated from total distance divided by total time is 68 km/h.
This weighted average concept is also frequently applied in mixtures, alligations, and relative motion problems in physics.
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