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, the distance covered by the bike is:

Choose the correct option.

Speed is defined as the ratio of distance travelled to time spent travelling. Because it has just one direction and no magnitude, speed is a scalar quantity.

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

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

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

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

Total time of journey = Time1 +  Time 2

$$\begin{gathered} \Rightarrow 8=\frac{x}{60}+\frac{x}{80} \\ \Rightarrow 8=\frac{(4x+3x)}{240} \\ \Rightarrow 8=\frac{7x}{240} \\ \Rightarrow x =\frac{240\times 8}{7}=274 km \end{gathered}$$

Total distance  =2$\times 274=548 km$

The total distance covered by the car is 548 km.