28 miles downstream in 2 hours 12 miles upstream in 3 hours what would the be speed in still water
if boat speed is b and water speed is w,
28/(b+w) = 2
12/(b-w) = 3
b=9, w=5
check: 28/9 = 2 and 12/4 = 3
oops 28/14=2
To find the speed in still water, we need to understand the concept of relative velocity. Relative velocity is the velocity of an object with respect to another object. When a boat is moving downstream, its speed is the sum of its own speed in still water and the speed of the current. Similarly, when the boat is moving upstream, its speed is the difference between its own speed in still water and the speed of the current.
Let's assume the speed of the boat in still water is 'x' mph, and the speed of the current is 'y' mph.
Given that the boat travels 28 miles downstream in 2 hours, we can set up the equation:
28 miles = (x + y) mph * 2 hours
Simplifying the equation, we have:
14 = x + y
Similarly, when the boat travels 12 miles upstream in 3 hours, the equation becomes:
12 miles = (x - y) mph * 3 hours
4 = x - y
Now we have a system of equations to solve for x and y. By adding the two equations together, we can eliminate the variable 'y':
14 + 4 = x + y + x - y
18 = 2x
Dividing both sides by 2, we find:
x = 9
So, the speed of the boat in still water is 9 mph.