The respective ratio between the time taken by a boat to travel the same distance downstream in stream A and stream B is 8:7. The speed of the boat is 12 km/h and the speed of stream A is half the speed of stream B. What is the speed of stream B? (in km/h)

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Accepted Answer

Step 1: Let the stream speeds be $a$ (A) and $b$ (B) with $a=	frac{b}{2}$. The boat speed in still water is $12\,$km/h.

Step 2: Downstream speeds are $12+a$ for A and $12+b$ for B. For the same distance, time ratio equals the inverse of speed ratio, so

$\dfrac{	ext{time}_A}{	ext{time}_B}=\dfrac{12+b}{12+a}=\dfrac{8}{7}.$

Step 3: Substitute $a=	frac{b}{2}$:

$\dfrac{12+b}{12+	frac{b}{2}}=\dfrac{8}{7}.$

Step 4: Solve:

$7(12+b)=8\left(12+\dfrac{b}{2}ight)\Rightarrow 84+7b=96+4b\Rightarrow 3b=12\Rightarrow b=4.$

Thus the speed of stream B is $4\,$km/h.

FINAL_ANSWER: d

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