2. A car moves a distance of 200 m. It covers the first half of the distance at speed 40 km/h and the second half of distance at speed v. The average speed is 48 km/h. Find the value of v.

2. A car moves a distance of 200 m. It covers the first half of the distance at speed 40 km/h and the second half of distance at speed v. The average speed is 48 km/h. Find the value of v.

(a) 56 km/h

(b) 60 km/h

(c) 50 km/h

(d) 48 km/h

Answer :  (b) 60 km/h

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

\( 48 = \frac{200}{\frac{100}{40} + \frac{100}{v}} \)

\( 48 = \frac{2}{\frac{1}{40} + \frac{1}{v}} \)

\( \frac{1}{40} + \frac{1}{v} = \frac{2}{48} \)

\( \frac{1}{40} + \frac{1}{v} = \frac{1}{24} \)

\( \frac{1}{v} = \frac{1}{24} - \frac{1}{40} \)

\( \frac{1}{v} = \frac{40 - 24}{24 \times 40} \)

\( \frac{1}{v} = \frac{16}{24 \times 40} \)

\( \frac{1}{v} = \frac{1}{60} \)

\( v = 60 \text{ km/h} \)