The speed of two bodies are in ratio 2 : 3. If the difference in the  time taken to cover 50 m is 20 sec., then Find the difference in their speeds.

\(\frac{5}{12}\) m/sec

               S₁  :   S₂

Speed      2   :   3  (given) 

We know S ∝ \(\frac{1}{t}\)              

      S ⇒   2    :    3

      T ⇒   3    :    2  ⇒ 1R= 20sec (given)

              ↓          ↓

             ×20      ×20

              ↓          ↓

            60 s      40 s

Speed (S) = \(\frac{Distance (D)}{Time (T)}\)         

S₁ = \(\frac{50}{60}\) = \(\frac{5}{6}\) m/sec

S₂  = \(\frac{50}{40}\) = \(\frac{5}{4}\) m/sec

Difference in their speeds are =  \(\frac{5}{4}\) - \(\frac{5}{6}\)

                                               = \(\frac{30 - 20}{24}\) = \(\frac{10}{24}\)

                                               = \(\frac{5}{12}\) m/sec