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?
2 : 1
3 : 2
8 : 3
Cannot be determined
Explanation:
Let the mans 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.
| $\Rightarrow \left(x \times 8\dfrac{4}{5} \right)$ = $y$ x 4 |
| $\Rightarrow \dfrac{44}{5} x $ =4$ y $ |
| $\Rightarrow y $ =$ \dfrac{11}{5} x $. |
| $\therefore$ Required ratio =$ \left(\dfrac{y + x}{2} \right) $:$ \left(\dfrac{y - x}{2} \right) $ |
| =$ \left(\dfrac{16x}{5} \times\dfrac{1}{2} \right) $:$ \left(\dfrac{6x}{5} \times\dfrac{1}{2} \right) $ |
| =$ \dfrac{8}{5} $:$ \dfrac{3}{5} $ |
= 8 : 3.