On a 120 km road a car has an average speed of 60 km/h. It covers the first 30 km at 40 km/h and the next 70 km at 70 km/h. Find its average speed on the remaining stretch.

Step-by-step solution

1. 1

   Turn the overall average into a total time. Average speed is total distance over total time, so $t=\frac{120}{60}=2\text{ h}$ This is the key move: the given average is a time budget, not a speed to be averaged with the others.

2. 2

   Time the first segment. $t_1=\frac{30}{40}=0.75\text{ h}$

3. 3

   Time the second segment. $t_2=\frac{70}{70}=1\text{ h}$

4. 4

   Subtract to get the leftover distance and time. $s_3=120-30-70=20\text{ km},\qquad t_3=2-0.75-1=0.25\text{ h}$

5. 5

   Divide for the final speed. $v_3=\frac{20}{0.25}=80\text{ km/h}$ so the answer is D. Note that averaging $40$, $70$ and $80$ naively gives $63.3$, not $60$ — the correct average must weight by time, and $(0.75\cdot 40+1\cdot 70+0.25\cdot 80)/2=60$ confirms consistency.