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A car travels 80 km at the speed of 20 km/h and the next 30 km at the speed of 30 km/h. What is its average speed?
30 km/h
20 km/h
40 km/h
22 km/h
22 km/h
Calculate the time taken for each segment individually (80/20=4 hours, 30/30=1 hour), then divide total distance (80+30=110 km) by total time (4+1=5 hours).
Distance 1 (d1) = 80 km, Speed 1 (s1) = 20 km/h, Distance 2 (d2) = 30 km, Speed 2 (s2) = 30 km/h
Average Speed=Total TimeTotal Distance=s1d1+s2d2d1+d2
Calculate the time taken for each segment individually (80/20=4 hours, 30/30=1 hour), then divide total distance (80+30=110 km) by total time (4+1=5 hours).
Do not simply average the speeds by doing (20+30)/2=25 km/h, because the car travels different distances at each speed.
Calculate time taken for the first segment
Using the formula Time=SpeedDistance for the first part of the journey where distance is 80 km and speed is 20 km/h:
t1=2080=4 hours
Calculate time taken for the second segment
Similarly, calculate the time for the second part of the journey where distance is 30 km and speed is 30 km/h:
t2=3030=1 hour
Find total distance and total time
Add both distances to find the total distance, and add both time periods to find the total time taken for the entire trip:
Total Distance=80+30=110 km,Total Time=4+1=5 hours
Calculate the average speed
Apply the average speed formula by dividing total distance by total time:
Average Speed=5110=22 km/h
D is correct because the total distance of 110 km divided by the total time of 5 hours gives an average speed of 22 km/h.
In problems involving varying speeds over unequal distances, always calculate total distance and total time separately rather than taking the arithmetic mean of the speeds.
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