A man can row 6 km/hr in still water. If the speed of the current is 2 km/hr he takes 4 hours more in upstream than the downstream. The distance is?

Explanation:-

$$\eqalign{ & {\text{Speed of man in still water,}} \cr & \Rightarrow {\text{ }}x{\text{ }} = {\text{ }}6{\text{ }}km/h \cr & {\text{Speed of current , }} \cr & \Rightarrow y{\text{ }} = {\text{ }}2{\text{ }}km/h \cr & {\text{Let distance = M}} \cr & {\text{According to question}} \cr & {\text{Upstream time }} \cr & {\text{ = Downstream time + 4}} \cr & \frac{M}{4} = \frac{M}{8} + 4 \cr & \frac{M}{4} = \frac{M}{8} + 4 \cr & \frac{M}{4} = \frac{{M + 32}}{8} \cr & M = 32 \cr & \therefore {\text{Distance = 32 }}km \cr & \cr & {\text{Alternate }} \cr & x = 6\,km/hr \cr & y = 2\,km/hr \cr & D:U = \left( {6 + 2} \right):\left( {6 - 2} \right) = 2:1 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,\,{\text{unit}} \cr & {T_D}:{T_U} = \cr & 1{\text{ unit = 4 hours}} \cr & {{\text{T}}_D} = 1 \times 4 = 4\,{\text{hours}} \cr & {{\text{T}}_U} = 2 \times 4 = 8{\text{hours}} \cr & {\text{Distance = D}} \times {{\text{T}}_D} \cr & = \left( {6 + 2} \right) \times 4 = 32km \cr}$$