A man covered a certain distance in 3 parts with average speeds of 30 km/h, 60 km/h, and 90 km/h. What is his average speed over the entire journey, assuming equal distances?
49.09 km/h
For three equal distances covered at speeds \(v_1, v_2, v_3\), the average speed is the harmonic mean: \(\text{Average speed} = \frac{3}{\frac{1}{v_1}+\frac{1}{v_2}+\frac{1}{v_3}}\).
Here \(v_1=30, v_2=60, v_3=90\), so \(\frac{1}{30}+\frac{1}{60}+\frac{1}{90} = \frac{6}{180}+\frac{3}{180}+\frac{2}{180} = \frac{11}{180}\).
The average speed is \(\frac{3}{\frac{11}{180}} = \frac{3 \times 180}{11} = \frac{540}{11}\).
Calculating, \(\frac{540}{11} = 49.09\).
Hence, the answer is 49.09 km/h.
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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:
