A boat running upstream takes 8 hours 48 min to cover a certain distan

1.	A boat running upstream takes 8 hours 48 min 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 the speed of the water current respectively? (a) 2 : 1 (b) 3 : 1 (c) 8 : 3 (d) 4 : 3
Answer» (c) 8 : 3 Let the distance covered in one direction be x km. Then, speed upstream = \(\frac{x}{\frac{44}{5}}\) km/hr (8 hrs 48 min = \(8\frac{48}{60}=8\frac45\) hrs) = \(\frac{5x}{44}\) km/hr Speed downstream =\(\frac{x}4\) km/hr ∴ Speed of boat in still water = \(\frac12\bigg(\frac{5x}{44}+\frac{x}{4}\bigg)\) = \(\frac{8x}{44} = \frac{2x}{11}\) km/hr Speed of current = \(\frac12\bigg(\frac{x}{4}-\frac{5x}{44}\bigg)=\frac{3x}{44}\) km/hr ∴ Required ratio = \(\frac{2x}{11}:\frac{3x}{44}=8:3.\)

A boat running upstream takes 8 hours 48 min 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 the speed of the water current respectively? (a) 2 : 1 (b) 3 : 1 (c) 8 : 3 (d) 4 : 3

Answer»

(c) 8 : 3

Let the distance covered in one direction be x km.

Then, speed upstream = \(\frac{x}{\frac{44}{5}}\) km/hr

(8 hrs 48 min = \(8\frac{48}{60}=8\frac45\) hrs) = \(\frac{5x}{44}\) km/hr

Speed downstream =\(\frac{x}4\) km/hr

∴ Speed of boat in still water = \(\frac12\bigg(\frac{5x}{44}+\frac{x}{4}\bigg)\)

= \(\frac{8x}{44} = \frac{2x}{11}\) km/hr

Speed of current = \(\frac12\bigg(\frac{x}{4}-\frac{5x}{44}\bigg)=\frac{3x}{44}\) km/hr

∴ Required ratio = \(\frac{2x}{11}:\frac{3x}{44}=8:3.\)

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