A bike completes a journey in eight hours. It covers half of the distance at 60 kmph and the remaining half at 80 kmph speed. Then, what is the distance covered by the bike?

Given data:

Total time of journey = 8 hours

Speed of the bike for half distance = 60 km/hr

Speed of the bike for the remaining distance = 80 km/hr

Let the total distance be 2x.

Half of the distance = x

Let the time taken to complete the first half of the journey be Time1.

Time1 = $\frac{\mathrm{Distance}}{\mathrm{Speed}}$  

$\mathrm{Time}1=\frac{\mathrm{x}}{60}\mathrm{hrs}$

Let the time taken to complete the second half of the journey be Time2.

Time 2 = $\frac{\mathrm{Distance}}{\mathrm{Speed}}$

$\mathrm{Time}2=\frac{\mathrm{x}}{80}\mathrm{hrs}$

Total time of journey = Time1 +  Time 2

$\begin{array}{rcl} & \Rightarrow & 8=\frac{\mathrm{x}}{60}+\frac{\mathrm{x}}{80}\\ & \Rightarrow & 8=\frac{(4\mathrm{x}+3\mathrm{x})}{240}\\ & \Rightarrow & 8=\frac{7\mathrm{x}}{240}\\ & \Rightarrow & \mathrm{x}=\frac{240\times 8}{7}\\ & \Rightarrow & \mathrm{x}=274.3 \mathrm{km}\end{array}$

Total distance = 2 x 274.3 = 548.6 km.

The total distance covered by the car is approximately 548 km.