1. A car covers the first half of the distance between two places at 40 km/h and other half at 60 km/h. The average speed of the car is ?

1. A car covers the first half of the distance between two places at 40 km/h and other half at 60 km/h. The average speed of the car is ?

(a) 40 km/h

(b) 48 km/h

(c) 50 km/h

(d) 60 km/h

Answer :  (b) 48 km/h

\( t_1 = \frac{d/2}{40}, \quad t_2 = \frac{d/2}{60} \)

\( \text{Speed}_{avg} = \frac{\text{Total distance}}{\text{Total time}} \)

\( = \frac{d/2 + d/2}{t_1 + t_2} \)

\( = \frac{d}{\frac{d}{2 \cdot 40} + \frac{d}{2 \cdot 60}} \)

\( = \frac{d}{\frac{d}{80} + \frac{d}{120}} \)

\( = \frac{d}{d\left(\frac{1}{80} + \frac{1}{120}\right)} \)

\( = \frac{1}{\frac{1}{80} + \frac{1}{120}} \)

\( = \frac{1}{\frac{120 + 80}{80 x 120}} \)

\( = \frac{1}{\frac{200}{9600}} \)

\( = \frac{96}{2} \)

\( = 48 \text{ km/h} \)