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 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?
