A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km/h. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km/h. If the total time of travel is 40 min find the average speed of the man for the whole journey.

The correct option is D.

Step 1, Given data

Distance between the home and market = 2.5 km

Total time of travel = 40 min

Speed = 5 km/h and 7.5 km/h

Step 2, Finding the average speed

From home to market, the time taken is time = $\frac{d}{v}=\frac{2.5}{5}=\frac{1}{2}$hr $=30$ min.

He returns back with speed of 7.5 km/h in rest of time, that is, 10 minutes.

(40 min is total time to travell and 30 min is time taken in going to market so remaining time is 10 min.)

Distance = $7.5\times \frac{10}{60}=1.25km$

Average speed = $\frac{Totaldistance}{Totaltime}$

= $\frac{(2.5+1.25)km}{\left(\frac{40}{60}\right)hr}$

$=\frac{45}{8}=5.625$ km/hr.

Hence the average speed is 5.625 km/h