Question

A man covers a distance of 30 km at a speed of 75 km/h and a distance of 50 km at a speed of 60 km/h. What is his average speed for the whole journey? (correct to one decimal place)
1. 64.9 km/h
2. 62.8 km/h
3. 63.6 km/h
4. 67.5 km/h

Answer 1

Correct Answer - Option 1 : 64.9 km/h

Given:

In first case:

Speed(S₁) = 75 km/hr

Distance(D₁) = 30 km

In second case:

Speed(S₂) = 60 km/hr

Distance(D₂) = 50 km

Formula:

Average Speed = (Total Distance/Total Time)

Time = Distance/Speed

Calculation:

Total Distance = 30 + 50 = 80 km

According to the question:

In first case:

Time = \(\frac{{30}}{75}\) = \(\frac{{2}}{5}\) hrs

In second case,

Time = \(\frac{{50}}{60}\) = \(\frac{{5}}{6}\) hrs

Total Time = \(\frac{{2}}{5}\) + \(\frac{{5}}{6}\) = \(\frac{{12 + 25}}{30}\) = \(\frac{{37}}{30}\) hrs

Average Speed = (Total Distance/Total Time)

Average Speed = 80 × \(\frac{{30}}{37}\) = 64.86 = 64.9 km/hr (approx.)

∴ The average speed of whole journey is 64.9 km/hr.