Jayesh covers one-fourth of his journey at 20 km/h, another one-fourth at 10 km/h, and the rest at 70 km/h. What is his average speed?
22.4 km/h
Average speed \(=\dfrac{\text{total distance}}{\text{total time}}\). Let the whole journey be \(D\) km.
The three parts are: one-fourth \(\tfrac{D}{4}\) at 20 km/h, one-fourth \(\tfrac{D}{4}\) at 10 km/h, and the rest \(\tfrac{D}{2}\) at 70 km/h.
Time for each part (time = distance ÷ speed): \(t_1=\dfrac{D/4}{20}=\dfrac{D}{80}\), \(t_2=\dfrac{D/4}{10}=\dfrac{D}{40}\), \(t_3=\dfrac{D/2}{70}=\dfrac{D}{140}\).
Total time \(=D\left(\dfrac{1}{80}+\dfrac{1}{40}+\dfrac{1}{140}\right)\). Using LCM 560: \(\dfrac{1}{80}=\dfrac{7}{560},\ \dfrac{1}{40}=\dfrac{14}{560},\ \dfrac{1}{140}=\dfrac{4}{560}\).
Sum \(=\dfrac{7+14+4}{560}=\dfrac{25}{560}=\dfrac{5}{112}\), so total time \(=\dfrac{5D}{112}\) hours.
Average speed \(=\dfrac{D}{\tfrac{5D}{112}}=\dfrac{112}{5}=22.4\) km/h.
Hence, the average speed is 22.4 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:
