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Average speed when distances are same
Sai travels from her house to office at a speed of 50kmph. She suddenly returns home at a speed of 60kmph. What is her average speed?
S1 = 50
S2 = 60
Sa = 2(50×60)/(50+60)
= 54.54 kmph
Average speed when time is same
A man travels 400 km at 50kmph. He then travels another 320 km at 40kmph. What is the average speed?
Time taken for 400km = 400/50 = 8 hours
Time taken for 320km = 320/40 = 8 hours
Since the time is same in both cases, use the above formula to find out the average speed.
S1 = 50
S2 = 40
Sa = (50+40)/2 = 45kmph
Average speed when time or distance are not same
A man travels 200 km at a speed 40kmph. He then travels 300 km at 50 kmph. Find his average speed.
D1 = 200; D2 = 300
S1 = 40; S2 = 50
Substitute the values in the above equation, we get
Sa = (200+300)/[(200/40)+(300/50)]
Sa = 500/(5+6) = 45.45 kmph
Least time to meet in a circular race
T1, T2, T3, …. = Individual times taken by each racer to complete one circle.
Three persons participate in a race on a circular track of length 400m. They can run at a speed of 2mps, 4mps and 5mps respectively. How long will they take to meet in the starting point for the first time?
Time taken by each person to complete one circle
Person 1 = 400/2 = 200 seconds = T1
Person 2 = 400/4 = 100 seconds = T2
Person 3 = 400/5 = 80 seconds = T3
LCM(T1, T2, T3) = 400 seconds
Time taken by them to meet at starting point for the first time = 400 seconds.
Time taken to meet in a circular race for first time
RT1 = Relative time taken for first and second persons to meet.
RT2 = Relative time taken for second and third persons to meet.
Three persons participate in a race on a circular track of length 400m. They can run at a speed of 2mps, 4mps and 5mps respectively. How long will they take to meet for the first time?
RT1 = D/(S1 ~ S2); RT2 = D/(S2 ~ S3)
D = 400m, length of the track.
RT1 = 400/2 = 200 sec ; RT2 = 400/1 = 400 sec
LCM(RT1,RT2) = LCM(200,400) = 400
Time taken for them to meet for the first time = 400s