Question

A car moves with a speed of 30km/h for half an hour, 25km/h for one hour and 40km/h for two hours. Calculate the average speed?

Answer 1

Hint: Here we have to calculate the average speed when the car moves with the speed of 30km/h for half an hour, 25km/h for one hour and 40km/h for two hours.

Complete step by step solution: We use the formula of ‘distance’ and ‘average speed’.
Distance = speed ×time
Average speed = Total distance / Total time
To find average speed first we have to find the total distance and total time, so
The distance covered when he moves with a speed of 30km/h for half an hour,
Distance = 30 × (1/2) = 15km ----- (1)
The distance covered when he moves with a speed of 25km/h for one hour,
Distance = 25 × 1 = 25km ------- (2)
The distance covered when he moves with a speed of 40km/h for two hour,
Distance = 40 × 2 = 80km ------ (3)
 We get the total distance when we add equation (1), (2) and (3)
Total distance = 15km + 25km + 80km
                          = 120km ------- (4)
Now total time taken by car to travel the distance is = 0.5 + 1 + 2 = 3.5h ------ (5)
Hence, apply the formula of average speed, and put the values of total distance from equation (4) and total time from equation (5),

Average speed = 120 / 3.5
Average speed = 34.286 km/h

Note: We can use direct formula to find average speed, (when three speeds are given)
Average speed = $\dfrac{{3{s_1}{s_2}{s_3}}}{{{s_1}{s_2} + {s_2}{s_3} + {s_3}{s_1}}}$
$
   = \dfrac{{3 \times 30 \times 25 \times 40}}{{30 \times 25 + 25 \times 40 + 40 \times 30}} \\
   = \dfrac{{90000}}{{750 + 1000 + 1200}} \\
   = \dfrac{{90000}}{{2950}} \\
   = 34.2 \\
 $