TIME AND DISTANCE ­ ­- Important Notes/Formulae

(1) Circular track motion – Time taken to meet for the first time is given below

(a) If 2 persons run in the SAME direction

(b) If 2 persons run in OPPOSITE direction

(c) If 3 persons run in SAME direction

(2) Clocks - Angle between the Hr hand and Min hand at H : M
α = 30H – (11m/2)

(3) Clocks – At what time between ‘T’ and ‘T+1’ hrs, does the angle between the Hr hand and min hand is ‘β’ ?
β = Difference between (6x) and [30T + (x/2)] , Form this eqn find ‘x’.
Therfore at T : x the angle between the hands will be β.

(4) If a person travels distance of ‘m’ at a speed of ‘a’ and a distance of ‘n’ at a speed of ‘b’, then
Avg speed = ab(m+n) / (ma+nb)

(5) 2 persons a and b start from A and B towards each other, they meet after ‘t’ secs. a takes ‘t1’secs to meet the point B after meeting b. Similarly b takes ‘t2’ secs to meet A, after meeting a. Then,
t = √(t1*t2)

(6) If a person travels to a Distance ‘D’ at ‘u’ Kmph, he is late by ‘p’ hrs.
If he travels at ‘v’ Kmph, he is late by ‘q’ hrs. Then,
D = uv(p+q) / (u+v)

(7) If speedof a boat is upstream is ‘u’ and downstream is ‘v’, then
Speed of boat in still water = (u+v)/2
Speed of stream = (u-v)/2