A bus travel $$\frac 13$$​ of the distance initially at a speed of 40 km/h, the next $$\frac 13$$​ of the distance 50 km/h, and the final $$\frac13$$​ of the distance at 60 km/h. Find the average speed of the bus for the entire journey. (Rounded off to two decimal places)

Correct option is A

Given:

Speed in first one-third of journey = 40km/hr

Speed in second one-third of journey = 50km/hr

Speed in last one-third of journey = 60km/hr

Formula Used:

​$$Time = \ \frac{Distance}{Speed}$$​​

Solution:

Let the distance of each journey be $$x$$​​

Then time taken in first one-third of journey = $$\frac{x}{40}$$​​

Time taken in second one-third of journey = $$\frac{x}{50}$$​​

Time taken in last one-third of journey =$$\frac{x}{60}$$​​

Total time taken for whole journey =$$\frac{x}{40} +\frac{x}{50}+\frac{x}{60}$$​​

​$$= x (\frac{1}{40} +\frac{1}{50}+\frac{1}{60})$$​​

​$$= x (\frac{15+12+10}{600})$$​​

​$$= (\frac{37x}{600})$$​​

Total distance travelled =$$x+x+x = 3x$$​​

Average speed of bus =$$\frac{3x}{(\frac{37x}{600})}$$​​

​$$= 3\times \frac{600}{37} = 48.65km/hr$$​​