A boat travels 24 km upstream in 6 hours and 20 km downstream in 4 hours . Then the speed of boat in still water and the speed of water/current are respectively

Options

A. 4 kmph and 3 kmph
B. 4.5 kmph and 0.5 kmph
C. 4 kmph and 2 kmph
D. 5 kmph and 2 kmph

Answer

To solve the problem step by step, we will calculate the speed of the boat in still water and the speed of the water/current based on the given upstream and downstream distances and times.

### Step 1: Calculate the speed upstream and downstream

1. **Speed upstream (S_U)**:
- Distance = 24 km
- Time = 6 hours
- Speed upstream (S_U) = Distance / Time = 24 km / 6 hours = 4 km/h

2. **Speed downstream (S_D)**:
- Distance = 20 km
- Time = 4 hours
- Speed downstream (S_D) = Distance / Time = 20 km / 4 hours = 5 km/h

### Step 2: Set up the equations for the speed of the boat and the speed of the current

Let:
- Speed of the boat in still water = S_B
- Speed of the water/current = S_W

From the definitions:
- Speed upstream (S_U) = S_B - S_W
- Speed downstream (S_D) = S_B + S_W

### Step 3: Substitute the calculated speeds into the equations

1. From the upstream speed:
- 4 km/h = S_B - S_W (1)

2. From the downstream speed:
- 5 km/h = S_B + S_W (2)

### Step 4: Solve the equations

Now, we can solve these two equations simultaneously.

1. From equation (1):
- S_B = 4 + S_W (3)

2. Substitute equation (3) into equation (2):
- 5 = (4 + S_W) + S_W
- 5 = 4 + 2S_W
- 5 - 4 = 2S_W
- 1 = 2S_W
- S_W = 1/2 km/h = 0.5 km/h

### Step 5: Find the speed of the boat in still water

Now substitute S_W back into equation (3):
- S_B = 4 + 0.5 = 4.5 km/h

### Final Answer

The speed of the boat in still water (S_B) is 4.5 km/h and the speed of the water/current (S_W) is 0.5 km/h.

### Summary of Results
- Speed of the boat in still water = 4.5 km/h
- Speed of the water/current = 0.5 km/h