A river 4.0 miles wide is following at the rate of 2 miles/hr. The minimum time taken by a boat to cross the river with a speed v=4 miles/hr (in still water) is approximately

Options

A. 1 hr and 9 minutes
B. 2 hr and 7 minutes
C. 1 hr and 12 minutes
D. 2 hr and 25 minutes

Explanation

To solve the problem of determining the minimum time taken by a boat to cross a river that is 4.0 miles wide and flowing at a rate of 2 miles/hr, with the boat's speed in still water being 4 miles/hr, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Width of the river (D) = 4 miles
- Speed of the river (Vr) = 2 miles/hr
- Speed of the boat in still water (Vb) = 4 miles/hr

2. **Determine the Effective Speed of the Boat**:
- To minimize the time taken to cross the river, the boat should head directly perpendicular to the riverbank. This means that the boat's speed in the direction of crossing (perpendicular to the river flow) will be its full speed, which is 4 miles/hr.
- The river's current will carry the boat downstream while it crosses, but this does not affect the time taken to cross the width of the river.

3. **Calculate the Minimum Time to Cross the River**:
- The time taken (T) to cross the river can be calculated using the formula:
\[ T = \frac{D}{Vb} \]
- Substituting the known values:
\[ T = \frac{4 \text{ miles}}{4 \text{ miles/hr}} = 1 \text{ hour} \]

4. **Conclusion**:
- The minimum time taken by the boat to cross the river is approximately **1 hour**.