A boat sails m miles upstream at the rate of r miles per hour. If the rate of the stream is s miles per hour, how long will it take the boat to return to its starting point?

Let the speed of the boat in still water be “x” miles/hr.

The speed of the stream is given as “s” miles/hr

Therefore,

Speed of the boat upstream = (x – s) miles/hr ….. (i)

Speed of the boat downstream = (x + s) miles/hr ……. (ii)

The distance covered by the boat while sailing upstream is given as  “m” miles

Speed of the boat upstream is given as “r” miles/hr …. (iii)

From (i) & (iii), we get

x - s = r

⇒ x = r + s ….. (iv)

Substituting the value of x in eq. (iii), we get

Speed of the boat downstream = (r + s + s) miles/hr = (r + 2s) miles/hr ….. (v)

Time = distance / speed

      = [m / (r + 2s)] hr