A boat covers 20 km in 4 hours along the current and 9 km in 3 hours against the current .What is the speed of the curent ?

Options

A. 2 kmph
B. 1 kmph
C. 1.5 kmph
D. 1.75 kmph

Answer

To find the speed of the current, we first need to determine the speed of the boat in still water and then use that information to calculate the speed of the current.

### Step 1: Calculate the speed of the boat along the current
The boat covers 20 km in 4 hours along the current.

\[ \text{Speed along the current} = \frac{\text{Distance}}{\text{Time}} = \frac{20 \text{ km}}{4 \text{ hours}} = 5 \text{ km/h} \]

### Step 2: Calculate the speed of the boat against the current
The boat covers 9 km in 3 hours against the current.

\[ \text{Speed against the current} = \frac{\text{Distance}}{\text{Time}} = \frac{9 \text{ km}}{3 \text{ hours}} = 3 \text{ km/h} \]

### Step 3: Set up the equations
Let \( b \) be the speed of the boat in still water and \( c \) be the speed of the current. We have the following equations based on the speeds:

1. \( b + c = 5 \) (speed along the current)
2. \( b - c = 3 \) (speed against the current)

### Step 4: Solve the equations
We can add the two equations to eliminate \( c \):

\[ (b + c) + (b - c) = 5 + 3 \]
\[ 2b = 8 \]
\[ b = 4 \text{ km/h} \]

Now, substitute \( b \) back into one of the equations to find \( c \):

\[ 4 + c = 5 \]
\[ c = 5 - 4 = 1 \text{ km/h} \]

### Conclusion
The speed of the current is \( 1 \text{ km/h} \).

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