A person covers 1/4 of his journey at the speed of 25 km/h, 1/2 of the journey at 40km/h and the remaining at the speed of 50 km/h. Find his average speed per hour for the whole journey (in km/h).
Given:
A person covers 1 / 4 of the journey at a speed of 25 km/hour, 1 / 2 of the journey at a speed of 40 km/hour, and the remaining part at a speed of 50 km/hour.
Used Formula:
Average speed = Total distance / Total time
Calculation:
Let the total distance be D km.
Distance covered at 25 km/hour = D/4 km
Distance covered at 40 km/hour = D/2 km
Distance covered at 50 km/hour = D - (D/4 + D/2) km = D/4 km
Time taken to cover D/4 km at 25 km/hour = (D/4) / 25 = D/100 hours
Time taken to cover D/2 km at 40 km/hour = (D/2) / 40 = D/80 hours
Time taken to cover D/4 km at 50 km/hour = (D/4) / 50 = D/200 hours
Total time = D/100 + D/80 + D/200
⇒ Total time = D (1/100 + 1/80 + 1/200)
⇒ Total time = D (0.01 + 0.0125 + 0.005)
⇒ Total time = D × 0.0275
Average speed = Total distance / Total time
⇒ Average speed = D / (D × 0.0275)
⇒ Average speed = 1 / 0.0275
⇒ Average speed = \(36\frac{4}{11}\) km/hour
∴ The correct answer is option (1).
Important Questions from Average Speed
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During a flight of 900 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 300 km/h and the time of flight increased by 30 min. The original duration of the flight was :
If a man travels from A to B at a speed of 50 km/h and returns by increasing his speed by 40%, then find his average speed (to 2 decimal places) for both the trips.
A man travels a distance of 420 km by train which moves at the speed of 75 km/h and returns back by car at the speed of 50 km/h. Find his average speed for the whole journey.
