Question

Sukumar travels from his house to his friend Raj's house which is at a distance of 10 km from his house in 15 minutes. He waited there for 15 minutes. and both of them moved toward Rajats house which was 20 km from Raj's house with an average speed of 40 km/hr. Find the average speed of Sukumar in this whole journey. 
1. 25 km / hr
2. 35.5 km / hr
3. 30 km / hr
4. 32.5 km / hr

Answer 1

Correct Answer - Option 3 : 30 km / hr

Concept:

Average speed: 

• The total path length traveled divided by the total time interval during which the motion has taken place is called the average speed of the particle.

\(Average\;speed\;\left( {\bar v} \right) = \frac{{total\;path\;length\;\left( S \right)}}{{total\;time\;taken\;\left( t \right)}}\)

Average velocity: 

• The ratio of net displacement to total time taken is called average velocity.

\(Average\;velocity\;\left( {\bar V} \right) = \frac{{{\rm{Net\;displacement\;}}\left( {{\rm{S'}}} \right)}}{{time\;taken\;\left( t \right)}}\)

Speed = \(\frac {Distance}{Time}\)

Calculation:

Given:

Distance covered by sukumar in reaching Raj house = 10 km

Distance covered by sukumar in reaching Rajat house = 20 km

Time taken by sukumar in reaching Raj house = 15 minutes

Waiting time = 15 minutes

Speed while reaching Rajat house = 40 km/hr

Time taken in reaching Rajat house = \(\frac {Distance}{Speed}\) = \(\frac {20}{40}\) = 0.5 hr = 30 minutes

Total time taken by Sukumar = 15 + 15 + 30 = 60 minutes = 1 hr

Total distance covered by Sukumar = 10 + 20 = 30 km

\(Average\;speed\;\left( {\bar v} \right) = \frac{{total\;path\;length\;\left( S \right)}}{{total\;time\;taken\;\left( t \right)}} = \frac {30}{1}\)

Average speed of sukumar = 30 km/hr