A boat sails m miles up stream 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?
Answers
If the rate of the stream is s miles per hour and the boat sails m miles upstream at the rate of r miles per hour, then the boat will return to its starting point at [m/(r+2s)] hour.
Step-by-step explanation:
Step 1:
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)
And,
Speed of the boat downstream = (x+s) miles/hr ……. (ii)
Step 2:
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)
Step 3:
Required formula:
Time = distance / speed
Thus, based on the above formula,
The time taken by the boat to return to its starting point i.e., that is it is the time taken by the boat to return downstream to the starting point, which is given by,
= [Distance covered while travelling downstream] / [speed of the boat down stream]
substituting the given value of distance and the value from (v), we get
= [m / (r + 2s)] hr
Hope this is helpful!!!!!