TSD

Basic TSD conversions (mins to hr)

15 mins = ¼ hr

30 mins = ½ hr

45mins = ¾ hr

48 mins = 4/5 hr

Speed time proportionality

Agar speed badhegi then time will decrease

S_a=2S_b then T_a = ½ T_b

S_a= 4/3 S_b then T_a = ¾ T_b

Time diff

Case 1 sath nikal rahe

Time diff

Case 2 dono alag nikal rahe

Case 3 bich mein kahi band hone ke wajah se late

Avg speed

= total dist / total time

Avg speed Case 1 - const time

Take arithmetic mean of the speeds

= a+b+c / 3

Avg speed Case 2 const distance

Take harmonic mean

= 3/ (1/a+1/b+1/c)

Shortcut if only 2 speeds are given

=2ab/a+b

Linear races

Shortcut for 3 bande only

Shortcut

L = ab/(a+b+c)

Imp- Trains from oppo direction

Tsquare = T1 * T2

Boats and streams

Downstream velo

Vd = Vb + Vw

Boats and streams

Upstream velo

Vu = Vb - Vw

Boats and streams

Boat velocity

Vb = (Vd + Vu)/2

Boats and streams

Water velocity

Vw = (Vd - Vu)/2

Boat and stream

Avg speed

= (Vb² - Vw²)/Vb

And for to and fro distance,

2D = ((Vb² - Vw²)/Vb) * t

Escalators

1. Stairs

2. Escalator

1. n=mt

2. a. Still man on escalator n = et

3. Right escalator (like downstream velo), n=(m+e)t

4. Wrong/against direction escalator (like upstream velo), n=(m-e)t

where,

n = nos of steps

m = Speed of men

e = Speed of escalator

t = time

NOTE: Agar sirf t diya hai then we can assume Distance like work rate and time. So that we can solve in m+e and m-e eq form to get separate m and e

Relative speed

Oppo direction: Add both speeds
Same direction: Subtract speeds
Note: Ensure both leaves at the same time from the location.
Ex.: Train 1(10km/hr) leaves from A at 9am and train 2 leaves from B at 10:30 am then pehle bring train 1 to 10×1.5hr = 15km distance from A then apply relative speed.