# A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

Let the man's rate upstream be x kmph and that downstream be y kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

$\Rightarrow x \times 8 \frac{4}{5}=y \times 4\\ \Rightarrow \frac{44}{5} x=4 y\\ \Rightarrow y=\frac{11}{5} x\\ \therefore Required ratio\\ =\frac{y+x}{2}: \frac{y-x}{2}\\ =\left(\frac{16 x}{5} \times \frac{1}{2}\right):\left(\frac{6 x}{5} \times \frac{1}{2}\right)\\ =\frac{8}{5}: \frac{3}{5}\\ =8: 3$

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