A swimmer start swimming from a sea shore in south direction and other one in east direction. Their distance becomes 100 km. in 2 hrs. If speed of one swimmer is 75% of another swimmer, find the speed of swimmer who swims faster ?

Options

A. 30 km./hr.
B. 40 km./hr.
C. 45 km./hr.
D. 60 km./hr.

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the problem
We have two swimmers: one swims south and the other swims east. The distance between them after 2 hours is 100 km. The speed of one swimmer is 75% of the other swimmer's speed.

### Step 2: Define variables
Let:
- The speed of the faster swimmer (swimmer B) be \( v_B \) km/h.
- The speed of the slower swimmer (swimmer A) be \( v_A \) km/h.

According to the problem, we have:
\[ v_A = 0.75 v_B \]
or
\[ v_A = \frac{3}{4} v_B \]

### Step 3: Express the speeds in terms of a variable
Let’s denote the speed of swimmer B as \( 4x \) km/h. Then, the speed of swimmer A will be:
\[ v_A = 3x \] km/h.

### Step 4: Calculate the distance covered by each swimmer
In 2 hours, the distance covered by swimmer A is:
\[ \text{Distance}_A = v_A \times 2 = 3x \times 2 = 6x \] km.

The distance covered by swimmer B is:
\[ \text{Distance}_B = v_B \times 2 = 4x \times 2 = 8x \] km.

### Step 5: Use the Pythagorean theorem
The total distance between the two swimmers after 2 hours is given as 100 km. According to the Pythagorean theorem:
\[ (6x)^2 + (8x)^2 = 100^2 \]

### Step 6: Solve the equation
Calculating the squares:
\[ 36x^2 + 64x^2 = 10000 \]
\[ 100x^2 = 10000 \]
\[ x^2 = 100 \]
\[ x = 10 \]

### Step 7: Find the speeds of the swimmers
Now we can find the speeds:
- Speed of swimmer A:
\[ v_A = 3x = 3 \times 10 = 30 \text{ km/h} \]
- Speed of swimmer B:
\[ v_B = 4x = 4 \times 10 = 40 \text{ km/h} \]

### Step 8: Conclusion
The speed of the faster swimmer (swimmer B) is:
\[ \boxed{40 \text{ km/h}} \]

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