A boat covers 18 km downstream in 3 hours . If speed of current is `33 (1)/(3)`% of its downstream speed . In what time will it cover a distance of 50 km upstream ?

Options

A. 50 hour
B. 40 hour
C. 30 hour
D. 25 hour

Explanation

To solve the problem step by step, we will follow the information given in the question and the video transcript.

### Step 1: Calculate the Downstream Speed
The boat covers 18 km downstream in 3 hours.

**Downstream Speed (S_d)** = Distance / Time
= 18 km / 3 hours
= 6 km/h

**Hint:** Remember that downstream speed is the speed of the boat in still water plus the speed of the current.

### Step 2: Define Variables
Let:
- Speed of the boat in still water = x km/h
- Speed of the current = y km/h

From the definition of downstream speed:
S_d = x + y
Thus, we have:
x + y = 6 km/h (1)

**Hint:** This equation represents the relationship between the speed of the boat and the speed of the current.

### Step 3: Calculate the Speed of the Current
According to the problem, the speed of the current (y) is 33.3% of the downstream speed (6 km/h).

y = 33.3% of 6 km/h
= (33.3/100) * 6
= 2 km/h

**Hint:** To convert a percentage to a decimal, divide by 100.

### Step 4: Calculate the Speed of the Boat in Still Water
Substituting the value of y into equation (1):

x + 2 = 6
x = 6 - 2
x = 4 km/h

**Hint:** Make sure to isolate the variable to find the speed of the boat in still water.

### Step 5: Calculate the Upstream Speed
The upstream speed (S_u) is given by the formula:
S_u = Speed of the boat in still water - Speed of the current
S_u = x - y
= 4 km/h - 2 km/h
= 2 km/h

**Hint:** Upstream speed is affected negatively by the current, so we subtract the current's speed.

### Step 6: Calculate the Time to Cover 50 km Upstream
Now, we need to find the time (T) taken to cover 50 km upstream:

T = Distance / Speed
T = 50 km / 2 km/h
T = 25 hours

**Hint:** Time can be calculated by dividing the distance by speed.

### Final Answer
The time required for the boat to cover 50 km upstream is **25 hours**.

---