Question : A boat running upstream takes 10 hours to cover a certain distance, while it takes 7 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and that of the water current, respectively?
Option 1: 17 : 5
Option 2: 3 : 17
Option 3: 2 : 17
Option 4: 17 : 3
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Correct Answer: 17 : 3
Solution : Given: Time to cover the distance upstream = 10 hr Time to cover the distance downstream = 7 hr Speed of boat downstream = Speed of boat in still water + speed of current Speed of boat upstream = Speed of boat in still water – speed of current Distance = Speed $\times$ Time Let the speed of the boat in still water be $x$ km/h and the speed of the stream of water be $y$ km/h. According to the question, $\frac{\text{Upstream Speed}}{\text{Downstream Speed}} = \frac{7}{10}$ ⇒ $\frac{x - y}{x + y} = \frac{7}{10}$ ⇒ $(x+y)\times7 = (x-y)\times10$ ⇒ $7x + 7y = 10x - 10y$ ⇒ $3x = 17y$ ⇒ $ \ \frac{x}{y} = \frac{17}{3}$ $\therefore x:y=17:3$ Hence, the correct answer is 17 : 3.
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