The ratio of the speed of boat in still water to the speed of stream is 16 :5. A boat goes 16.5 km in 45 minute upstream. Find the time taken by boat to cover the distance of 175 km downstream.

Let's denote the speed of the boat in still water as "B" km/h and the speed of the stream as "S" km/h. According to the problem, the ratio of these speeds is given as:

B : S = 16 : 5

Now, let's use this information to find the values of B and S. We can do this by setting up a proportion:

16/5 = B/S

Now, cross-multiply to find B:

16S = 5B

B = (16S)/5

B = (16/5)S

Now, we know the boat's speed in terms of the speed of the stream.

Next, let's calculate the boat's speed when going upstream (against the current). The boat's effective speed upstream is:

Effective speed upstream = Boat's speed in still water - Speed of the stream Effective speed upstream = [(16/5)S] - S

Now, we're given that the boat goes 16.5 km in 45 minutes upstream. Let's first convert the time to hours:

45 minutes = 45/60 hours = 3/4 hours

Now, we can use the formula: Distance = Speed × Time

Distance upstream = Effective speed upstream × Time 16.5 km = ([(16/5)S] - S) × (3/4)

Now, we can solve for S:

16.5 = ([(16/5)S] - S) × (3/4)

Now, simplify the equation:

16.5 = (3/4)[(16/5)S - S]

Now, multiply both sides by 4/3 to isolate the term with S:

(4/3) * 16.5 = (16/5)S - S

Now, calculate the left side:

(4/3) * 16.5 = 22

So, the equation becomes:

22 = (16/5)S - S

Now, combine the terms on the right side:

22 = (16/5 - 5/5)S

22 = (11/5)S

Now, solve for S:

S = (22 * 5) / 11

S = 10 km/h

Now that we have found the speed of the stream (S), we can calculate the boat's speed in still water (B):

B = (16/5)S B = (16/5) * 10 B = 32 km/h

Now, we know the boat's speed in still water (B) is 32 km/h, and the speed of the stream (S) is 10 km/h.

To find the time taken by the boat to cover the distance of 175 km downstream, we use the formula: Time = Distance / Speed

Time = 175 km / (B + S) Time = 175 km / (32 km/h + 10 km/h) Time = 175 km / 42 km/h Time = 25/3 hours

Now, convert hours to minutes:

Time = (25/3) * 60 minutes ≈ 500/3 minutes ≈ 166.67 minutes

Rounded to the nearest minute, the time taken by the boat to cover the distance of 175 km downstream is approximately 167 minutes, which is closest to 25 minutes. So, the answer is 25 minutes.