A boat on a river travels 16 miles downstream in only 2 hours. It takes the same boat 7 hours to travel 28 miles upstream. What are the speed of the boat and the speed of the current?
speed of boat --- x mph
speed of current -- y mph
16/(x+y) = 2
2x + 2y = 16
x + y = 8
28/(x-y) = 7
7x - 7y = 28
x-y = 4
add them:
2x = 12
x = 6
then mentally y = 2
the speed of the boat is 6 mph, and the current is 2 mph
To find the speed of the boat and the speed of the current, we can use a system of equations. Let's assume the speed of the boat is B and the speed of the current is C.
When the boat is traveling downstream, its effective speed is increased because it is traveling with the current. Therefore, the boat's speed downstream can be represented as B + C.
Similarly, when the boat is traveling upstream, its effective speed is decreased because it is traveling against the current. Therefore, the boat's speed upstream can be represented as B - C.
We now have two equations based on the given information:
Equation 1: (B + C) * 2 = 16 (downstream speed * time = distance traveled)
Equation 2: (B - C) * 7 = 28 (upstream speed * time = distance traveled)
Let's solve this system of equations step by step:
From Equation 1: (B + C) * 2 = 16, we can simplify and rewrite it as:
B + C = 8 (divide both sides by 2)
From Equation 2: (B - C) * 7 = 28, we can simplify and rewrite it as:
B - C = 4 (divide both sides by 7)
Now we have a system of equations:
B + C = 8
B - C = 4
We can solve this system by adding both equations together:
(B + C) + (B - C) = 8 + 4
2B = 12
B = 6
Now that we have the speed of the boat (B = 6), we can substitute it into one of the original equations, such as Equation 1: B + C = 8:
6 + C = 8
C = 8 - 6
C = 2
Therefore, the speed of the boat is 6 miles per hour, and the speed of the current is 2 miles per hour.