A boat takes two hours to travel 8 km down and 8 km up the river when the water is still. How much time will the boat take to make the same trip when the river starts flowing at 4 kmph?

Options

A. 2 hour
B. 2 hour 40 minute
C. 3 hour
D. 3 hour 40 minute

Answer

To solve the problem step by step, we will first determine the speed of the boat in still water and then calculate the time taken for the trip when the river is flowing.

### Step 1: Determine the speed of the boat in still water
The boat takes 2 hours to travel a total distance of 16 km (8 km downstream and 8 km upstream).

- Speed of the boat in still water (Vb) can be calculated using the formula:

\[ Vb = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{16 \text{ km}}{2 \text{ hours}} = 8 \text{ km/h} \]

### Step 2: Determine the effective speeds downstream and upstream
When the river is flowing at 4 km/h, the effective speeds of the boat will change:

- Downstream speed (Vd) = Speed of the boat + Speed of the river
\[ Vd = Vb + Vr = 8 \text{ km/h} + 4 \text{ km/h} = 12 \text{ km/h} \]

- Upstream speed (Vu) = Speed of the boat - Speed of the river
\[ Vu = Vb - Vr = 8 \text{ km/h} - 4 \text{ km/h} = 4 \text{ km/h} \]

### Step 3: Calculate the time taken for downstream and upstream trips
Now we can calculate the time taken for each leg of the trip:

- Time taken to travel downstream (T1):
\[ T1 = \frac{\text{Distance}}{\text{Speed}} = \frac{8 \text{ km}}{12 \text{ km/h}} = \frac{2}{3} \text{ hours} \]

- Time taken to travel upstream (T2):
\[ T2 = \frac{\text{Distance}}{\text{Speed}} = \frac{8 \text{ km}}{4 \text{ km/h}} = 2 \text{ hours} \]

### Step 4: Calculate the total time for the trip
The total time for the round trip when the river is flowing is:
\[ \text{Total Time} = T1 + T2 = \frac{2}{3} \text{ hours} + 2 \text{ hours} = \frac{2}{3} + \frac{6}{3} = \frac{8}{3} \text{ hours} \]

### Step 5: Convert total time into minutes
To convert \(\frac{8}{3}\) hours into minutes:
\[ \frac{8}{3} \text{ hours} = \frac{8}{3} \times 60 \text{ minutes} = 160 \text{ minutes} \]

### Final Answer
The boat will take \(\frac{8}{3}\) hours or 160 minutes to make the same trip when the river starts flowing at 4 km/h.

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