Question:
Mr. John went to a nearby city by a train at a speed of 70 km/h and returned home by a taxi at a speed of 50 km/h. What is his average speed in total journey?
Correct Answer
58 1/3 km/h or 58.33 km/h
Solution And Explanation
Solution
Given, speed while going to the city = 70 km/h
And speed while returing to the home = 50 km/h
Thus, average speed = ?
Calculation of Average Speed using formula when to and fro speed are given
We know that
Average Speed = 2 × a × b/a + b
Where, a and b are the speeds
Thus, Average Speed for the given journey
= 2 × 70 × 50/70 + 50 km/h
= 700 175/12 3 km/h
= 175/3 km/h
= 58 1/3 km/h or 58.33 km/h
Thus, Average Speed = 58 1/3 km/h or 58.33 km/h Answer
Alternate Method: Calculation of Average Speed when to and fro speed are given
Given, speed while going to the city = 70 km/h
And speed while returing to the home = 50 km/h
Thus, average speed = ?
Let the distance between home and the city = m km
Let the time taken in the journey from the home to the city (To Journey) = t1 hour
Let the time taken in the journey from the city to the home (Fro Journey) = t2 hour
We know that, time = Distance/Speed
Therefore, time taken in the joureny from home to the city (t1) = m/70 hour - - - - (i)
Therefore, time taken in the joureny from city to home (t2) = m/50 hour - - - - (ii)
Thus, total time in the complete journey = t1 + t2
The Average Speed = Total distance covered/Total time taken
∴ Average Speed = m + m/t1 + t2
After subsituting the values of t1 and t2 from equation (i) and (ii) in the above expression we get
m + m/m/70 + m/50 km/h
= 2 m/50 m + 70 m/70 × 50 km/h
= 2 m/120 m/3500 km/h
= 2 m × 3500/120 m km/h
= 700 175/12 3 km/h
= 175/3 km/h
= 58 1/3 or 58.33 km/h
Thus, Average speed of Mr. John = 58 1/3 or 58.33 km/h Answer
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