Question

5. X started a journey to a village 9 km away from his house. After travelling 6 km at a speed of 40km/hr., the car stopped running. He then travelled by rickshaw at a speed of 10 km/ hr. After travelling a distance of 2 km, he left the rickshaw and covered the remaining distance on foot at a speed of 4 km/hr. Find the average speed.

Answer 1

5. X started a journey to a village 9 km away from his house. After travelling 6 km at a speed of 40 km/hr., the car stopped running. He then travelled by rickshaw at a speed of 10 km/hr. After travelling a distance of 2 km, he left the rickshaw and covered the remaining distance on foot at a speed of 4 km/hr. Find the average speed.

Average speed equals:

$$v _ {a} = \frac {S}{t}$$

S – total distance

t – total time

$$S = S _ {1} + S _ {2} + S _ {3} = 9 \text{ km} \quad \text{- total distance}$$ $$S _ {1}, S _ {2}, S _ {3} \quad \text{- distance for each part}$$ $$S _ {1} = 6 \text{ km} \quad \text{- the distance for traveling by car,}$$ $$S _ {2} = 2 \text{ km} \quad \text{- the distance for traveling by rickshaw,}$$ $$S _ {3} = 9 - 6 - 2 = 1 \text{ km} \quad \text{- the distance for traveling by foot,}$$ $$t = t _ {1} + t _ {2} + t _ {3} \quad \text{- total time}$$

Let’s find time for each part:

$$t _ {1} = \frac {S _ {1}}{v _ {1}} = \frac {6}{40} = \frac {3}{20} \text{ hours} \quad \text{- the time for traveling by car}$$ $$t _ {2} = \frac {S _ {2}}{v _ {2}} = \frac {2}{10} = \frac {1}{5} \text{ hours} \quad \text{- the time for traveling by rickshaw}$$ $$t _ {3} = \frac {S _ {3}}{v _ {3}} = \frac {1}{4} \text{ hours} \quad \text{- the time for traveling by foot}$$ $$v _ {1}, v _ {2}, v _ {3} \quad \text{- speeds for each part}$$

Now we can plug in total distance and total time in the formula for average speed:

$$v _ {a} = \frac {9}{\frac {3}{20} + \frac {1}{5} + \frac {1}{4}} = 15 \text{ km/h}$$

Answer: $v_{a} = 15\frac{\text{km}}{\text{h}}$