Speed of boat in still water is 12 meter/sec and speed of current is 10 meter/sec. Find total time taken by boat to cover 550 meter if boat goes `(1)/(5) th` of distance in upstream and rest in downstream?

Options

A. 1 min 5 sec
B. 1 min 30 sec
C. 1 min 15 sec
D. 120 sec

Answer

To solve the problem step-by-step, we will use the information provided about the boat's speed in still water, the speed of the current, and the distances traveled upstream and downstream.

### Step 1: Identify the speeds
- Speed of the boat in still water (x) = 12 m/s
- Speed of the current (y) = 10 m/s

### Step 2: Calculate the effective speeds for upstream and downstream
- **Upstream speed** = Speed of boat - Speed of current = \( x - y = 12 - 10 = 2 \) m/s
- **Downstream speed** = Speed of boat + Speed of current = \( x + y = 12 + 10 = 22 \) m/s

### Step 3: Determine the distances traveled upstream and downstream
- Total distance = 550 meters
- Distance traveled upstream = \( \frac{1}{5} \) of total distance = \( \frac{1}{5} \times 550 = 110 \) meters
- Distance traveled downstream = Total distance - Distance upstream = \( 550 - 110 = 440 \) meters

### Step 4: Calculate the time taken for each part of the journey
- **Time taken upstream** = Distance upstream / Upstream speed = \( \frac{110}{2} = 55 \) seconds
- **Time taken downstream** = Distance downstream / Downstream speed = \( \frac{440}{22} = 20 \) seconds

### Step 5: Calculate the total time taken
- Total time = Time upstream + Time downstream = \( 55 + 20 = 75 \) seconds

### Step 6: Convert total time into minutes and seconds
- 75 seconds = 1 minute and 15 seconds

### Final Answer
The total time taken by the boat to cover 550 meters is **1 minute and 15 seconds**.

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