The current of a river is 2 miles per hour. A boat travels to a point 24 miles upstream and back in 5 hours. What is the speed of the boat in still water?
To find the speed of the boat in still water, we can use the formula:
Speed of the boat in still water = (Speed of the boat downstream + Speed of the boat upstream) / 2
Let's break down the problem:
1. Let's assume that the speed of the boat in still water is 'B' miles per hour.
2. We are given that the current of the river is 2 miles per hour. So, the speed of the boat downstream would be the sum of the speed of the boat in still water and the speed of the current, which is B + 2 miles per hour.
3. Similarly, the speed of the boat upstream would be the difference between the speed of the boat in still water and the speed of the current, which is B - 2 miles per hour.
4. The boat travels to a point 24 miles upstream and then comes back. So, the total distance traveled by the boat is 2 times 24 miles, which is 48 miles.
5. We are given that the total time taken for the round trip is 5 hours.
Now, we can use the formula to calculate the speed of the boat in still water:
Speed of the boat in still water = (Speed of the boat downstream + Speed of the boat upstream) / 2
= ((B + 2) + (B - 2)) / 2
= (2B) / 2
= B
So, the speed of the boat in still water is B miles per hour.
To find the value of B, we need more information about the time taken for each leg of the trip.