The boat is moving with a current of 15 km/h and the speed of the stream is 2.5 km/h. Find the speed of the boat against the current.
Understand the Problem
The question is asking us to find the speed of a boat when it is moving against a current. Given the current's speed and the boat's speed with the current, we will use the formula for relative speed to calculate the required speed against the current.
Answer
The speed of the boat against the current is $12.5 \text{ km/h}$.
Answer for screen readers
The speed of the boat against the current is $12.5 \text{ km/h}$.
Steps to Solve
- Identify the speeds given in the problem
We know the boat's speed with the current is 15 km/h, and the speed of the current is 2.5 km/h.
- Set up the equation for the speed against the current
The speed of the boat against the current can be calculated using the formula: $$ \text{Speed against current} = \text{Speed with current} - \text{Speed of current} $$
- Plug in the known values
Substituting the values into the equation: $$ \text{Speed against current} = 15 \text{ km/h} - 2.5 \text{ km/h} $$
- Calculate the speed against the current
Perform the subtraction to find the speed against the current: $$ \text{Speed against current} = 12.5 \text{ km/h} $$
The speed of the boat against the current is $12.5 \text{ km/h}$.
More Information
When a boat moves with a current, its speed is the sum of its speed in still water and the current's speed. Conversely, when moving against the current, you subtract the current's speed from the boat's speed in still water.
Tips
- Forgetting to subtract the speed of the current when calculating the speed against it. Always remember to use subtraction for speeds against the current.
- Mixing up the values: Double-check that the speed with the current and the current's speed are correctly assigned.
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