The sum of the speed of boat A downstream and that of, Boat B upstream is 27km/h. If the speed of boat A in still water is 3km/h less than that of boat B, what is the ratio、 of the speed of boat A in still water to that of boat B in still water? (Consider, the speed of the current to be constant.)

Options

A. `4:5`
B. `2:5`
C. `2:3`
D. `3:5`

Answer

To solve the problem step by step, we will define the variables and set up the equations based on the information given.

### Step 1: Define Variables
Let:
- \( x_1 \) = speed of boat A in still water (in km/h)
- \( x_2 \) = speed of boat B in still water (in km/h)
- \( y \) = speed of the current (in km/h)

### Step 2: Set Up the Equations
From the problem, we know:
1. The speed of boat A in still water is 3 km/h less than that of boat B:
\[ x_1 = x_2 - 3 \]

2. The sum of the speed of boat A downstream and boat B upstream is 27 km/h:
- Speed of boat A downstream = \( x_1 + y \)
- Speed of boat B upstream = \( x_2 - y \)

Therefore, we can write the equation:
\[ (x_1 + y) + (x_2 - y) = 27 \]
Simplifying this gives:
\[ x_1 + x_2 = 27 \]

### Step 3: Substitute \( x_1 \) in the Equation
Now, substitute \( x_1 \) from the first equation into the second equation:
\[ (x_2 - 3) + x_2 = 27 \]
This simplifies to:
\[ 2x_2 - 3 = 27 \]

### Step 4: Solve for \( x_2 \)
Add 3 to both sides:
\[ 2x_2 = 30 \]
Now, divide by 2:
\[ x_2 = 15 \]

### Step 5: Find \( x_1 \)
Now that we have \( x_2 \), we can find \( x_1 \):
\[ x_1 = x_2 - 3 = 15 - 3 = 12 \]

### Step 6: Find the Ratio
Now we can find the ratio of the speed of boat A to the speed of boat B:
\[ \text{Ratio} = \frac{x_1}{x_2} = \frac{12}{15} = \frac{4}{5} \]

### Final Answer
The ratio of the speed of boat A in still water to that of boat B in still water is \( \frac{4}{5} \).

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