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Shortcut 40:

    \(S=\frac DT\)

S = Speed
D = Distance
T = Time taken
Question:
A man travels 200 km in 4 hours. What is the speed in which he travelled?
Answer:
S = 200/4 = 50 kmph
Question:
A cat runs at a speed of 3 meter per second. How long will it take to cross 3 km?
Answer:
T = D/S = 3 x 1000 / 3 = 1000 seconds

Shortcut 41:

Relative speed in same direction

\(S_1\sim S_2\)

Question:
Two cars start from same point and travels in same direction at speeds 40kmph and 50kmph. What is the relative speed between them?
Answer:
Relative speed = 50~ 40 = 10 kmph.

Shortcut 42:

Relative speed in opposite direction

      \( S_1+S_2\)     

Question:
Two cars start from same point and travels in opposite directions at speeds 40kmph and 50kmph. What is the relative speed between them?
Answer:
Relative speed = 50 + 40 = 90 kmph.

Shortcut 43:

Time taken to catch a thief

   \(T=D/(S_1\sim S_2)\)

Question:
A thief standing 50 away from a police starts running away from him at a speed of 2 m/s. The police suddenly starts chasing him at a speed of 3m/s. How long will the police take to catch the thief?
Answer:
D = 50m
S1 = 3
S2 = 2
Time taken, T = 50/(3-2)
= 50 seconds

Shortcut 44:
Time taken to meet from opposite direction

     \(T=D/(S_1+S_2)\)

Question:
Two persons starts from their home 3km apart and walk towards each other at a speed of 2mps and 3mps. How long (in minutes) will they take to meet each other?
Answer:
D = 3000m
S1 = 2mps
S2 = 3mps
T = 3000/(2+3)
= 600 seconds
Time taken in minutes = 600/60 = 10 minutes.