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
A car runs first 275 km at an average speed of 50 km/h and the next 315 km at an average speed of 70 km/h. What is the average speed ( in km/h) for the entire journey?
Akhil rides first 12 km at a speed of 16 km/h and further 6 km at a speed of 20 km/h. Find his average speed (in km/h).
Shyam drives his car 30 km at a speed of 45 km/h and, for the next 1 h 20 m, he drives it at a speed of 51 km/h. Find his average speed (in km/h) for the entire journey.
X and Y travel a distance of 90 km each such that the speed of Y is greater than that of X. The sum of their speeds is 100 km/h and the total time taken by both is 3 hours 45 minutes. The ratio of the speed of X to that of Y is:
If a man travels at \(\frac{1}{x}\) km/h on a journey and returns at \(\rm \frac{1}{x^2}\) km/h, then his average speed for the journey is:
