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?

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? Correct Answer m/r+2s

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  
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