Ajay walks at a speed of 4 km/hr. He doubles his speed after reaching exactly half way. He walks for 12 hours in all. What is the total distance travelled by him?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 64 km
The two halves are of equal distance but are walked at different speeds, so the time of each half is found separately and the two times add up to 12 hours. Let the total distance be \(D\) km.
First half at 4 km/h: time \(\displaystyle =\frac{D/2}{4}=\frac{D}{8}\) h
Second half at 8 km/h: time \(\displaystyle =\frac{D/2}{8}=\frac{D}{16}\) h
\(\displaystyle \frac{D}{8}+\frac{D}{16}=12\), that is, \(\displaystyle \frac{3D}{16}=12\)
\(D=64\) km
Tip: The average speed over two equal distances is not the plain average of the speeds (6 km/h). It is \(\displaystyle \frac{2\times4\times8}{4+8}=\frac{16}{3}\) km/h, and \(\displaystyle \frac{16}{3}\times12=64\) km.