Introduction to Boat Speed and Current Speed

Understanding the speed of a boat in still water and the speed of the current is crucial for several applications in physics, engineering, and sports. This problem involves a boat whose speed changes according to whether it's moving along or against the current. Here, we will solve a specific problem to find these exact speeds. This solution can be applied to other similar scenarios as well.

The Problem

Given a boat that can row at 8 km/hr along the current and 6 km/hr against the current, we need to determine the speed of the boat in still water and the speed of the current.

Setting Up the Equations

To solve this problem, we can set up a system of equations based on the given information. Let's define the variables:

- b as the speed of the boat in still water (in km/hr)

- c as the speed of the current (in km/hr)

According to the information given:

The speed of the boat along the current is: ( b c 8 ) km/hr The speed of the boat against the current is: ( b - c 6 ) km/hr

Solving the Equations

Let's proceed step by step to solve these equations.

Step 1: Add the two equations

Adding the two equations will help eliminate c and find the value of b.

[ (b c) (b - c) 8 6 ]

This simplifies to:

[ 2b 14 ]

Therefore:

[ b 7 , text{km/hr} ]

This is the speed of the boat in still water.

Step 2: Find the value of c

Now, we can substitute the value of b into one of the original equations to find c.

Using the equation ( b c 8 ):

[ 7 c 8 ]

This simplifies to:

[ c 1 , text{km/hr} ]

This is the speed of the current.

Final Answer

Thus, the speed of the boat in still water is 7 km/hr and the speed of the current is 1 km/hr.

Solving Additional Problems

The same approach can be used to solve similar problems. Here are a few additional examples:

Example 1

A boat can row 14 km/hr along the current and 6 km/hr against the current. What are the speed of the boat in still water and the speed of the current?

Let's denote the speed of the boat in still water as x and the speed of the current as y.

According to the given information:

[ x y 14 , text{km/hr} ]

[ x - y 6 , text{km/hr} ]

Adding these two equations:

[ (x y) (x - y) 14 6 ]

This simplifies to:

[ 2x 20 ]

Therefore:

[ x 10 , text{km/hr} ]

Substituting back into one of the original equations:

[ 10 y 14 ]

This gives:

[ y 4 , text{km/hr} ]

Example 2

A boat can row 18 km/hr along the current and 6 km/hr against the current. What are the speed of the boat in still water and the speed of the current?

Let x be the speed of the boat in still water and y be the speed of the current.

According to the given information:

[ x y 18 , text{km/hr} ]

[ x - y 6 , text{km/hr} ]

Adding these two equations:

[ (x y) (x - y) 18 6 ]

This simplifies to:

[ 2x 24 ]

Therefore:

[ x 12 , text{km/hr} ]

Substituting back into one of the original equations:

[ 12 y 18 ]

This gives:

[ y 6 , text{km/hr} ]

Conclusion

By understanding the relationship between the speed of the boat in still water and the speed of the current, one can solve a variety of problems related to this concept. This method can be applied to find the speed of the boat and current in any given scenario, ensuring a comprehensive understanding of the underlying principles.

Related Keywords

boat speed current speed still water speed