Question : The distance between two places A and B is 14 km. A boat travels from A to B downstream and then returns from B to A upstream which takes a total of 3 hours 44 minutes for the entire journey. If the speed of the current is 2 km/hr, then what is the speed of the boat, in km/hr, in still water?
Option 1: $8$
Option 2: $7$
Option 3: $7 \frac{1}{2}$
Option 4: $6 \frac{1}{2}$
Correct Answer: $8$
Solution :
Given: Distance = 14 km
Let the speed of the boat be $x$ km/hr.
According to the question,
$\frac{14}{(x + 2)} + \frac{14}{(x - 2)} = 3\frac{44}{60}$
⇒ $\frac{14(x - 2 + x + 2)}{(x^2 - 4)} = 3 + \frac{44}{60}$
⇒ $\frac{28x}{(x^2 - 4)}= \frac{56}{15}$
⇒ $15x = 2x^2 - 8$
⇒ $2x^2 - 15x - 8 = 0$
⇒ $2x^2 - 16x + x - 8 = 0$
⇒ $2x(x - 8) + 1 (x - 8) = 0$
⇒ $(2x + 1) (x - 8) = 0$
⇒ $x - 8 = 0$ [Since speed can not be negative]
⇒ $x = 8$ km/hr
Hence, the correct answer is 8.
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