A boat takes total 5 hours to cover 24 km downstream and 12 km upstream but it takes total 5.5 hours to cover 12 km downstream and 24 km upstream. What is speed of current (in km/h)?

1

\(\frac{24}{D}\) + \(\frac{12}{U}\) = 5 .... (i)

\(\frac{12}{D}\) + \(\frac{24}{U}\) = 5.5

in upstream travel 36 km in 6 hours

U = \(\frac{36}{6}\) = 6 km/h

put in (i)

\(\frac{24}{D}\) + \(\frac{12}{6}\) = 5

\(\frac{24}{D}\) = 3

D = 8 km/h or speed of current = \(\frac{8 - 6}{2}\) = 1 km/h

OR

by shifting method

     D              U       

  24 km       12 km         5h

     ↓               ↓               ↓

   -12            +12         +0.5

     ↓               ↓               ↓

    12             24            5.5

     ↓               ↓               ↓

   -12            +12         +0.5

     ↓               ↓               ↓

     0            36 km         6

x + y = 8

x - y = 6

2x = 14

 x = 7

 y = 1