A man paddles his canoe 10 km upstream in 2 hours. Then, he paddles downstream
18 km in 2 hours. What is the speed of the canoe in still water and what is the speed of the current?
let S equal speed in still water , and C equal the speed of the current
S - C = 10 km / 2 hr = 5 kph
S + C = 18 km / 2 hr = 9 kph
adding equations (to eliminate C) ... 2 S = 14 kph
solve for S , then substitute back to find C
What is the answer?
To find the speed of the canoe in still water and the speed of the current, we need to use the concept of relative velocities.
Let's assume the speed of the canoe in still water is "c" km/h, and the speed of the current is "x" km/h.
When the canoe paddles upstream, it opposes the current. So, the effective speed is the difference between the canoe's speed and the current's speed: (c - x) km/h.
Using the formula: Distance = Speed * Time,
we can calculate the time it took for the canoe to paddle upstream: 10 km = (c - x) km/h * 2 hours.
Similarly, when the canoe paddles downstream, it gets an extra push from the current. So, the effective speed is the sum of the canoe's speed and the current's speed: (c + x) km/h.
Again, using the formula: Distance = Speed * Time,
we can calculate the time it took for the canoe to paddle downstream: 18 km = (c + x) km/h * 2 hours.
Now, we have two equations:
1) 10 = (c - x) * 2
2) 18 = (c + x) * 2
Simplifying equation 1, we get:
10 = 2c - 2x
Simplifying equation 2, we get:
18 = 2c + 2x
Now, we can solve these two equations simultaneously to find the values of c and x.
Adding equation 1 and equation 2, we eliminate x:
10 + 18 = 2c - 2x + 2c + 2x
28 = 4c
Dividing both sides by 4, we get:
c = 7
Now, substituting the value of c = 7 into equation 1:
10 = 2(7) - 2x
10 = 14 - 2x
Rearranging the equation, we get:
2x = 14 - 10
2x = 4
x = 2
Therefore, the speed of the canoe in still water is 7 km/h, and the speed of the current is 2 km/h.