A man travels for 5 hours 15 minutes. If he covers the first half of the journey at 60 km/hr and rest at 45 km/hr. Find the total distance travelled by him ?

Answer: Option D

Let ther distance covered be 2x km
$$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$$
Time taken to covers the first half and second half of the journey in t₁ hours and t₂ hours
$$\begin{array}{rl}& \Rightarrow \frac{a}{60}=t_1.....(i)\\ & \Rightarrow \frac{a}{45}=t_2.....(ii)\end{array}$$
Adding (i) and (ii) we get
$$\begin{array}{rl}& \iff \frac{a}{60}+\frac{a}{45}=t_1+t_2\\ & \iff \frac{a}{60}+\frac{a}{45}=5\frac{15}{60}\\ & \iff \frac{a}{60}+\frac{a}{45}=5\frac{1}{4}\\ & \iff \frac{3a+4a}{180}=\frac{21}{4}\\ & \iff 7a=\frac{21}{4}\times 180\\ & \Rightarrow a=\frac{21\times 180}{4\times 7}\\ & \Rightarrow a=135\text{ km}\end{array}$$
∴ Length of total journey :
= (2 × 135) km
= 270 km