A bus travels 1/3 of distance initially at a speed of 40 km/h, the next 1/3 of the distance 50km/h, - SSC STUDY

A bus travels 1/3 of distance initially at a speed of 40 km/h, the next 1/3 of the distance 50km/h, and the final 1/3 of the distance at 60 km/h. Find the average speed of the bus for the entire journey. (Rounded off to two decimal places)

Options
a) 48.65 km/h
b) 46.85 km/h
c) 54.13 km/h
d) 51.43 km/h

Solution

Let the Total Distance = 3D
Formula: Distance = Speed x Time

Time of First Journey: T₁ = Distance/ Time = D/40
Time of First Journey: T₂ = Distance/ Time = D/50
Time of First Journey: T₃ = Distance/ Time = D/60
Total Time = T₁ + T₂+T₃ = $\frac {D}{40} + \frac {D}{50} + \frac {D}{60}$
$\frac {15D+12D+10D}{600} = \frac {37D}{600}$

Average Speed = Total Distance / Total Time
= $\frac {3D} { \frac {37D}{600}} = \frac {1800}{37} = 48.64$

Answer: 48.64 KM/Hr