Speeds of a boat along the current and against the current are 16 km/hr and 12 km/hr respectively. What is the speed (in km/hr) of the current?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the speed of the current, we can use the following formulas:

1. Speed of the boat along the current (downstream) = Speed of the boat + Speed of the current
2. Speed of the boat against the current (upstream) = Speed of the boat - Speed of the current

Let's denote:
- Speed of the boat = B km/hr
- Speed of the current = C km/hr

From the information given in the question:
- Speed of the boat along the current (downstream) = 16 km/hr
- Speed of the boat against the current (upstream) = 12 km/hr

Now, we can set up the equations based on the above formulas:

1. B + C = 16 (Equation 1)
2. B - C = 12 (Equation 2)

Now, we can solve these two equations step by step.

### Step 1: Add the two equations
Adding Equation 1 and Equation 2:
(B + C) + (B - C) = 16 + 12

This simplifies to:
2B = 28

### Step 2: Solve for B
Now divide both sides by 2:
B = 28 / 2
B = 14 km/hr

### Step 3: Substitute B back into one of the equations
Now we can substitute B back into Equation 1 to find C:
14 + C = 16

### Step 4: Solve for C
Now, subtract 14 from both sides:
C = 16 - 14
C = 2 km/hr

### Final Answer
The speed of the current is 2 km/hr.

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