Question : Mr. Robert goes to his office everday by a cycle and returns home everyday by an electric cycle. If the speed of the cycle is 15 km/h and the speed of the electric bike is 25 km/h, then find his average speed in to and fro journey.
Correct Answer 18 3/4 km/h or 18.75 km/h
Solution & Explanation
Solution
Given, speed of cycle while going to the office = 15 km/h
And speed of the electric bike while returing to the home = 25 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 × 15 × 25/15 + 25 km/h
= 750 75/40 4 km/h
= 75/4 km/h
= 18 3/4 km/h or 18.75 km/h
Thus, Average Speed = 18 3/4 km/h or 18.75 km/h Answer
Alternate Method: Calculation of Average Speed when to and fro speed are given
Given, speed of cycle while going to the office = 15 km/h
And speed of the electric bike while returing to the home = 25 km/h
Thus, average speed = ?
Let the distance between Robert's home and his office = a km
Let the time taken in the journey from Robert's home to his office (To Journey) = t1 hour
Let the time taken in the returning journey i.e. from Robert's office to his home (Fro Journey) = t2 hour
We know that, time = Distance/Speed
Therefore, time taken in the joureny from Robert's home to his office (t1) = a/15 hour - - - - (i)
Therefore, time taken in the returning journey i.e. from Robert's office to his home (t2) = a/25 hour - - - - (ii)
Thus, total time in the complete journey = t1 + t2
The Average Speed = Total distance covered/Total time taken
∴ Average Speed = a + a/t1 + t2
After subsituting the values of t1 and t2 from equation (i) and (ii) in the above expression we get
a + a/a/15 + a/25 km/h
= 2 a/15 a + 25 a/15 × 25 km/h
= 2 a/40 a/375 km/h
= 2 a × 375/40 a km/h
= 750/40 km/h
= 75/4 km/h
= 18 3/4 or 18.75 km/h
Thus, Average speed of Robert in complete journey = 18 3/4 or 18.75 km/h Answer
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