A boat sails 'm' miles upstream at the rate of 'r' miles per hour. The rate
of the stream is 's' miles per hour. How long will it take the boat to return to its starting point?
I didn't understand why m/r+2s instead I got m/ r-s
upstream time is
m/(r-s)
downstream time is
m/(r+s)
To find the time it will take for the boat to return to its starting point, we need to calculate the time it takes for the boat to sail upstream and the time it takes for the boat to sail downstream.
Let's start with the time it takes for the boat to sail upstream. We know that the boat is sailing 'm' miles upstream at a rate of 'r' miles per hour. The effective speed of the boat when sailing upstream is the difference between its rate and the rate of the stream, which is 'r - s'.
Time taken to sail upstream = Distance / Speed
= 'm' / ('r - s') hours
Next, let's calculate the time it takes for the boat to sail downstream. When the boat is sailing downstream, its effective speed is the sum of its rate and the rate of the stream, which is 'r + s'.
Time taken to sail downstream = Distance / Speed
= 'm' / ('r + s') hours
Now, to find the total time taken for the boat to return to its starting point, we need to add the time taken to sail upstream and the time taken to sail downstream.
Total time taken = Time taken to sail upstream + Time taken to sail downstream
= 'm' / ('r - s') + 'm' / ('r + s') hours
So, the total time taken for the boat to return to its starting point is 'm' / ('r - s') + 'm' / ('r + s') hours.
To find out how long it will take the boat to return to its starting point, we need to analyze the motion of the boat when it's going upstream and when it's going downstream.
Let's consider the boat's speed when it's going upstream. Since the boat is sailing against the current, its effective speed is reduced. The speed of the boat relative to the water is given by the difference between the boat's rate and the stream's rate.
So the boat's speed upstream is (r - s) miles per hour.
Now, we can calculate the time it takes for the boat to sail upstream (against the current) using the formula:
Time = Distance / Speed.
The distance the boat sails upstream is 'm' miles, and the speed of the boat upstream is (r - s) miles per hour.
Therefore, the time it takes for the boat to sail upstream is m / (r - s) hours.
Next, let's consider the boat's speed when it's going downstream. Since the boat is sailing with the current, its effective speed is increased. The speed of the boat relative to the water is given by the sum of the boat's rate and the stream's rate.
So the boat's speed downstream is (r + s) miles per hour.
Similarly, we can calculate the time it takes for the boat to sail downstream (with the current) using the formula:
Time = Distance / Speed.
The distance the boat sails downstream is 'm' miles, and the speed of the boat downstream is (r + s) miles per hour.
Therefore, the time it takes for the boat to sail downstream is m / (r + s) hours.
Since we are interested in the total time it takes for the boat to return to its starting point, we need to add the time it takes for the boat to sail upstream and the time it takes for the boat to sail downstream.
Total time = Time upstream + Time downstream
= m / (r - s) + m / (r + s)
Simplifying this equation further or substituting any values you may have for 'm', 'r', and 's', will give you the answer to how long it will take the boat to return to its starting point.