The problem asks for the ratio of the speed of the boat in still water to the speed of the water. We are given the speed downstream (\(x\)) and the speed upstream (\(y\)).
Let:
We know the following relationships:
Using the given variables:
To find the speed of the boat (\(B\)) and the speed of the water (\(C\)), we can solve the system of linear equations:
The question requires the ratio of the speed of the boat in still water (\(B\)) to the speed of the water (\(C\)).
Ratio = \(\frac{B}{C}\)
Substitute the values we found for \(B\) and \(C\):
\(\text{Ratio} = \frac{\frac{x + y}{2}}{\frac{x - y}{2}}\)Simplify the expression:
\(\text{Ratio} = \frac{x + y}{x - y}\)This matches Option 3.
A boat sails 15 km of a river towards upstream in 5 hours. How long (in hours) will it take to cover the same distance downstream, if the speed of river is one-fourth the speed of the boat in still water?
The speed of boat upstream is 5 kmph. Its speed in still water is 10 kmph. How many minutes will it take to row 25 km downstream?
Sudha can travel a certain distance downstream in 6 hours by boat and return to the starting point in 9 hours. If the stream flows at a speed of 3 km/h, how long (in hours) will it take to cover a distance of 67.5 km in still water?
The downstream speed of a boat is 20 km/hr and the speed of stream is 4 km/hr. What will be the total time taken by the boat to cover 160 km downstream and 96 km upstream?
The ratio of the speeds of a boat in still water and the speed of the river is 3 ∶ 1. The boat takes 45 minutes for a round trip journey. Find the distance of the whole trip if the speed of the stream is 4 km/hr.