As part of his journey, a person travels 120 km at 80 km/h, the next 100 km at 40 km/h, and comes back to the starting point at 75 km/h. The average speed of the person throughout the journey (approximately) is:

The correct answer is 63.46 km/h.

The key formula for average speed over an entire journey is:

\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}}

Let's carefully identify all the segments of the journey.

Step 1: Identify the Journey Segments

- Leg 1: 120 km at 80 km/h
- Leg 2: 100 km at 40 km/h
- Return trip: Back to the starting point at 75 km/h

The person ends up 120 + 100 = 220 km away from the starting point after the first two legs. So the return trip covers 220 km at 75 km/h.

Step 2: Calculate the Total Distance

\text{Total Distance}=120+100+220=440\text{km}

Step 3: Calculate the Time for Each Leg

Using \text{Time}=\frac{\text{Distance}}{\text{Speed}} :

Time for Leg 1:
t_1=\frac{120}{80}=1.5\text{hours}

Time for Leg 2:
t_2=\frac{100}{40}=2.5\text{hours}

Time for Return Trip:
t_3=\frac{220}{75}=\frac{44}{15}\approx 2.9333\text{hours}

Step 4: Calculate the Total Time

\text{Total Time}=1.5+2.5+\frac{44}{15}=4+\frac{44}{15}

Converting 4 to a fraction with denominator 15:

\text{Total Time}=\frac{60}{15}+\frac{44}{15}=\frac{104}{15}\text{hours}

Step 5: Calculate the Average Speed

\text{Average Speed}=\frac{440}{\frac{104}{15}}=440\times \frac{15}{104}=\frac{6600}{104}

\text{Average Speed}=\mathrm{63.4615...}\approx 63.46\text{km/h}

Why not just average the three speeds?
A common mistake is to add the three speeds and divide by 3, which gives (80 + 40 + 75)/3 ≈ 65 km/h. This is wrong because the person spends different amounts of time on each leg. The person spends the most time on Leg 2 (2.5 hours at 40 km/h), which pulls the true average speed lower than a simple arithmetic mean. The correct method always uses total distance ÷ total time.

Therefore, the average speed for the entire journey is approximately 63.46 km/h.