A boat takes 2 hours to travel 30 km down a river, then 6.5 hours to return. How fast is the river flowing?
B=velocity of boat
R=velocity of river
2*(B+R)=30
6.5*(B-R)=30
Solve for B and R
To find the speed of the river, we need to determine the difference between the boat's speed downstream and its speed upstream.
Let's assume the boat's speed in still water is denoted by "B" (in km/h), and the speed of the river is denoted by "R" (also in km/h).
When the boat is going downstream, it benefits from the flow of the river, which increases its effective speed. So, the boat's speed downstream would be (B + R) km/h.
Conversely, when the boat is going upstream, it has to fight against the flow of the river, which reduces its effective speed. So, the boat's speed upstream would be (B - R) km/h.
Given that the boat takes 2 hours to travel 30 km downstream and 6.5 hours to return, we can set up the following equations:
2(B + R) = 30 (Equation 1)
6.5(B - R) = 30 (Equation 2)
Now, we can solve this system of equations to find the values of "B" and "R."
From Equation 1:
B + R = 15 (Divide both sides by 2)
From Equation 2:
6.5B - 6.5R = 30
Let's multiply Equation 2 by 2 to eliminate the decimal:
13B - 13R = 60 (Equation 3)
Now, we have two equations:
B + R = 15 (Equation 1)
13B - 13R = 60 (Equation 3)
We can use these equations to solve for "B" and "R" simultaneously.