A boat can cover a distance of 7.2 km downstream and 3.2 km upstream in 2 hours. It can also cover 1.5 km downstream and 0.6 km upstream in 24 minutes. What is the speed of the boat when going downstream (in km/hr)?

6

Let the speed of boat = U km/hr

          speed of current = V km/hr

ATQ,     \(\frac{7.2}{U+V}\) + \(\frac{3.2}{U-V}\) = 120 minutes ------- (i)

            \(\frac{1.5}{U+V}\) + \(\frac{0.6}{U-V}\) = 24 minutes --------(ii)

Equate both the equations by multiplying eq. (i) by 6 and eq. (ii) by 32

            \(\frac{43.2}{U+V}\) + \(\frac{19.2}{U-V}\) = 720 ----------(i)

            \(\frac{48}{U+V}\)  + \(\frac{19.2}{U-V}\) = 768 -------- (ii)

                                               \(\frac{4.8}{U+V}\) = 48  ------- (ii) [ (ii) - (i)]

                                                                  U + V = \(\frac{4.8}{48}\) × 60

                                                                           = 6 km/hrs