60 km
64 km
Ajay's journey is split into two equal distance segments. He covers the first half at 4 km/hr and the second half at 8 km/hr. The total travel time is 12 hours.
Let the total distance be \(D\) km. The journey is divided into two parts, each of length \(\frac{D}{2}\) km.
Time taken for the first \(\frac{D}{2}\) km at 4 km/hr:
\( \text{Time}_1 = \frac{\frac{D}{2}}{4} = \frac{D}{8} \, \text{hours}\)
Time taken for the second \(\frac{D}{2}\) km at 8 km/hr:
\( \text{Time}_2 = \frac{\frac{D}{2}}{8} = \frac{D}{16} \, \text{hours}\)
The sum of the times for both halves equals the total journey time of 12 hours:
\(\frac{D}{8} + \frac{D}{16} = 12\)
Combine the fractions:
\(\frac{2D}{16} + \frac{D}{16} = 12\)
\(\frac{3D}{16} = 12\)
Solve for \(D\):
\(3D = 12 \times 16\)
\(3D = 192\)
\(D = \frac{192}{3}\)
\(D = 64\)
Ajay traveled a total distance of 64 km.
Correct Answer: 64 km