A boat on a river travels downstream between two points, 70 mi apart, in one hour. The return trip against the current takes
2
1
2
hours. What is the boat's speed (in still water)
To find the speed of the boat in still water, we need to consider the concept of relative speed.
Let's assume the speed of the boat in still water is "x" mph, and the speed of the current is "y" mph. When traveling downstream, the boat's speed is increased by the speed of the current, and when traveling upstream, the boat's speed is decreased by the speed of the current.
When traveling downstream, the boat covers the distance of 70 miles in 1 hour, so its effective speed is (x + y) mph (speed of the boat + speed of the current).
When traveling upstream, the boat covers the same distance of 70 miles in 2.5 hours, so its effective speed is (x - y) mph (speed of the boat - speed of the current).
Using the formula: speed = distance / time, we can write the following equations:
(x + y) = 70 / 1 (equation 1)
(x - y) = 70 / 2.5 (equation 2)
Simplifying equation 1, we get:
x + y = 70
Simplifying equation 2, we get:
x - y = 28
Now, we can solve these equations simultaneously to find the values of x and y.
Adding the two equations together:
(x + y) + (x - y) = 70 + 28
2x = 98
x = 49
Substituting the value of x into equation 1:
49 + y = 70
y = 21
Therefore, the speed of the boat in still water is 49 mph.