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1. 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. m/(r + 2s)
- B. m/(r + 2s)
- C. m/(r + 2s)
- D. m/(r + 2s)
Answer: Option A
Explanation:
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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