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 person covers a certain distance at the speed of 60 kmph and returns to the starting point at a speed of 40 kmph . Find the average speed (in km/hour) of the person for the whole journey.
A train runs at a speed of 28 kmph for 4 hours and 30 kmph for 5 hours and the remaining 40 kms in one hour. What is the average speed per hour?
Kapil travels for 4.5 hours at a speed of 50 km / h and 7.5 hours at a speed of 70 km / h. At the end of it, he finds that he covered only 6/7 of the total distance. At what average speed should he travel so that the remaining distance traveled in 5 hours?
An express train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long it take to reach its destination 600 km from the starting point?
A car has to cover 125 kms in 5 hours. What will be the average speed of the car if it has covered 90 kms in the first 3 hours?
