A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in still water?

Options

A. 40 minutes
B. 1 hour
C. 1 hr 15 min
D. 1 hr 30 min

Answer

To solve the problem step by step, we need to find the speed of the boat in still water based on the information given about its speed against and along the current. Then, we will calculate the time it takes to travel a certain distance in still water.

### Step 1: Calculate the speed of the boat against the current
The boatman goes 2 km against the current in 1 hour.

- **Speed against the current (upstream)** = Distance / Time = 2 km / 1 hour = 2 km/h

### Step 2: Calculate the speed of the boat along the current
The boatman goes 1 km along the current in 10 minutes.

- First, convert 10 minutes into hours:
- 10 minutes = 10/60 hours = 1/6 hours
- Now, calculate the speed along the current (downstream):
- **Speed along the current (downstream)** = Distance / Time = 1 km / (1/6 hours) = 1 km × (6/1) = 6 km/h

### Step 3: Calculate the speed of the boat in still water
The speed of the boat in still water can be calculated using the formula:
- **Speed in still water** = (Speed downstream + Speed upstream) / 2

Substituting the values:
- Speed in still water = (6 km/h + 2 km/h) / 2 = 8 km/h / 2 = 4 km/h

### Step 4: Calculate the time to travel 5 km in still water
Now, we need to find out how long it will take to go 5 km in still water.

- **Time** = Distance / Speed
- Here, Distance = 5 km and Speed = 4 km/h

Substituting the values:
- Time = 5 km / 4 km/h = 5/4 hours = 1.25 hours

### Step 5: Convert time into minutes
To convert 1.25 hours into minutes:
- 1 hour = 60 minutes
- 0.25 hours = 0.25 × 60 minutes = 15 minutes
- Therefore, 1.25 hours = 1 hour + 15 minutes = 1 hour 15 minutes

### Final Answer
The time it will take to go 5 km in still water is **1 hour and 15 minutes**.

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