The car traveled the first 30 minutes at 60 km/h and the next 20 minutes at 90 km/h. Find the average speed of the car for the whole trip.
t₁ = 30 min = 0.5 h
v₁ = 60 km/h
t₂ = 20 min = 1/3 h
v₂ = 90 km/h
Split the motion into two legs and find the distance of each separately.
Average speed is the total distance divided by the total time. You cannot add the speeds 60 and 90 km/h.
1. Find the distance of each leg:
$$s_1 = v_1 \cdot t_1 = 60 \cdot 0.5 = 30 \text{ km}$$$$s_2 = v_2 \cdot t_2 = 90 \cdot \frac{1}{3} = 30 \text{ km}$$2. Total distance and total time:
$$s = s_1 + s_2 = 30 + 30 = 60 \text{ km}$$$$t = t_1 + t_2 = 30 + 20 = 50 \text{ min} = \frac{5}{6} \text{ h}$$3. Average speed:
$$v = \frac{s}{t} = \frac{60}{5/6} = 72 \text{ km/h}$$v = 72 km/h