Question

A car departed from city A to city D. After 3.5 hours when it reached town C, the road was blocked due to maintenance work. The car returned in the same way back and reached B. From there it took a shortcut and reached D after 4 hours. Observe the diagram below showing the route of the car and find the average speed of the car.​

Answer 1

Solution :

Case 1 :-

• Time taken from A to C = 3.5 hrs

• Distance between A to C = 70 km

$\large \boxed{\boxed{ \sf Speed_1= \frac{Distance}{time}}} \\ \\ \implies \sf \frac{70}{3.5} \\ \\\implies \sf20 \: km/hr$

Case 2 :-

• Time taken from C to D = 4 hrs

• Distance between C to D = 80 km

$\large\boxed{ \boxed{ \sf Speed_2= \frac{Distance}{time}}} \\ \\ \implies \sf \frac{80}{4} \\ \\\implies \sf20 \: km/hr$

Now

$\large\sf Speed_{average} = \frac{speed_1 +speed_2}{2} \\ \\ \sf \implies \frac{20 + 20}{2} \\ \\\sf \implies \frac{40}{2} \\ \\\sf \implies20 \\ \\ \large\implies \boxed{ \boxed{ \sf Speed_{average} = 20 \: km/hr}}$