The Mad River flows at a rate of 3 km/h. In order for a boat to travel 78.2 km upriver and then return in a total of 8 hr, how fast must the boat travel in still water?
what formula would be used to solve this problem?
V = D/T would be the path to a solution.
Letting T = D/V, you know that
78.2/(V + 3) + 78.2/(V - 3) = 8 hr.
Solve for V, the speed of the boat in still water.
Is the answer 10 km/h?
To solve this problem, we can use the concept of relative velocity.
Let's break down the problem into two parts: the boat going upstream and the boat going downstream.
When the boat is going upstream, it is travelling against the current of the Mad River. The effective speed of the boat is reduced by the speed of the current.
When the boat is going downstream, it is travelling with the current of the Mad River. The effective speed of the boat is increased by the speed of the current.
Let's assume that the boat's speed in still water is B km/h.
Now, let's use some formulas to solve the problem:
1. Upstream trip:
The boat's effective speed = Boat's speed in still water - Speed of current
Effective speed = (B - 3) km/h
Distance travelled = 78.2 km (given)
Time taken = Distance / Speed = 78.2 / (B - 3) hours
2. Downstream trip:
The boat's effective speed = Boat's speed in still water + Speed of current
Effective speed = (B + 3) km/h
Distance travelled = 78.2 km (same as upstream trip)
Time taken = Distance / Speed = 78.2 / (B + 3) hours
Total time taken = Time taken upstream + Time taken downstream = 8 hours (given)
Now, we can set up an equation based on the above information:
78.2 / (B - 3) + 78.2 / (B + 3) = 8
This equation considers the fact that the total time taken is 8 hours.
To solve this equation, we can use algebraic methods such as cross-multiplication and simplification.
Once we solve the equation, we will find the value of B, which represents the boat's speed in still water.