ratio between speed of boat in still water to speed of stream is 5:2. if 224 km is travelled bydownstream in 4 hours then find the difference between speed of boat in still water and speed of stream?
The Correct Answer and Explanation is :
The correct answer is: B – S = 40 – 16 = 24 \, \text{km/h}
Let the speed of the boat in still water be ( B ) km/h and the speed of the stream be ( S ) km/h. The ratio between the speed of the boat in still water to the speed of the stream is given as 5:2. Thus, we can express:
[
B : S = 5 : 2
]
This means:
[
B = 5x \quad \text{and} \quad S = 2x
]
where ( x ) is a constant.
The downstream speed, which is the sum of the boat’s speed in still water and the speed of the stream, is ( B + S ). Therefore, the downstream speed is:
[
B + S = 5x + 2x = 7x
]
We are told that the boat travels 224 km downstream in 4 hours. So, using the formula ( \text{Distance} = \text{Speed} \times \text{Time} ), the downstream speed is:
[
\frac{224}{4} = 56 \, \text{km/h}
]
Thus, we have:
[
7x = 56
]
Solving for ( x ):
[
x = \frac{56}{7} = 8
]
Now that we have ( x = 8 ), we can find the speed of the boat in still water (( B )) and the speed of the stream (( S )):
[
B = 5x = 5 \times 8 = 40 \, \text{km/h}
]
[
S = 2x = 2 \times 8 = 16 \, \text{km/h}
]
Finally, the difference between the speed of the boat in still water and the speed of the stream is:
[
B – S = 40 – 16 = 24 \, \text{km/h}
]
Explanation:
The problem is solved by first expressing the boat’s speed in still water and the stream’s speed in terms of a common constant ( x ), based on the given ratio (5:2). Knowing that the total downstream speed is the sum of these two, and given the distance and time taken for the downstream journey, we use the relationship between distance, speed, and time to find ( x ). Once ( x ) is known, the individual speeds of the boat in still water and the stream are calculated, and their difference is determined. The answer is 24 km/h.