A person covers a certain distance by bus at 45 km/h and immediately returns to the starting point by car at a speed of 80 km/h. What is his average speed during the whole journey?

Given:

Speed of bus = 45 km/h

Speed of car = 80 km/h

Formula Used:

Average Speed = \(\frac{\text { Total Distance Covered }}{\text { Total Time Taken }}\)

Calculation:

Let the distance covered by person by bus be d.

When the person travels by bus the time taken can be calculated as:

Time Taken = Distance/Speed = \(d \over 45\)

When the person travels by car, the distance will be same. So, time taken can be calculated as:

Time Taken = Distance/Speed = \(d \over 80\)

The total time taken for the entire journey can be calculated as:

Total time taken = \(d \over 45\) + \(d \over 80\)

Also, the Total Distance covered = 2d

So, Average speed can be calculated as:

⇒ \(\frac{2 d}{\frac{d}{45}+\frac{d}{80}}\)

⇒ \(\frac{2 d}{16 d + 9d \over 720}\)

⇒ \(\frac{2 d}{\frac{25 d}{720}} \)

⇒ \( \frac{2 d \times 720}{25 d} \)

⇒ 57.6 km/h

 ∴ The average speed for the whole journey is 57.6 km/h.

 Shortcut Trick

If distance is constant, the average speed = \(\frac{2 \times S_1 \times S_2}{(S_1 + S_2)}\) [ where S1 and S2 are two speeds ]

Average speed = \(\frac{2 \times 45 \times 80}{(45 + 80)}\) = 288/5 = 57.6 km/hr