Speed of a motorboat in still water is 45 km./hr. If it takes 1 hour 20 min. to travel 80 km. downstream, how much time will it take to cover the same distance the stream ?

Options

A. 3 hour
B. 1 hour 20 minute
C. 2 hour 40 minute
D. 2 hour 55 minute

Answer

To solve the problem, we need to find out how long it will take for the motorboat to cover the same distance upstream after determining the speed of the stream.

### Step-by-Step Solution:

1. **Convert Time to Hours**:
The time taken to travel downstream is given as 1 hour 20 minutes. We need to convert this to hours.
\[ 1 \text{ hour } 20 \text{ minutes} = 1 + \frac{20}{60} = 1 + \frac{1}{3} = \frac{4}{3} \text{ hours} \]

**Hint**: To convert minutes to hours, divide the number of minutes by 60.

2. **Calculate Downstream Speed**:
The distance traveled downstream is 80 km. To find the downstream speed, we use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{80 \text{ km}}{\frac{4}{3} \text{ hours}} = 80 \times \frac{3}{4} = 60 \text{ km/hr} \]

**Hint**: Remember that speed is calculated as distance divided by time.

3. **Determine the Speed of the Stream**:
Let the speed of the stream be \( s \) km/hr. The speed of the boat in still water is 45 km/hr. The downstream speed is the sum of the speed of the boat and the speed of the stream:
\[ \text{Downstream Speed} = \text{Speed of Boat} + \text{Speed of Stream} \]
\[ 60 = 45 + s \implies s = 60 - 45 = 15 \text{ km/hr} \]

**Hint**: When calculating downstream speed, add the speed of the boat and the speed of the stream.

4. **Calculate Upstream Speed**:
The upstream speed is the speed of the boat minus the speed of the stream:
\[ \text{Upstream Speed} = \text{Speed of Boat} - \text{Speed of Stream} = 45 - 15 = 30 \text{ km/hr} \]

**Hint**: For upstream speed, subtract the speed of the stream from the speed of the boat.

5. **Calculate Time to Travel Upstream**:
Now, we need to find the time taken to travel the same distance (80 km) upstream:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{80 \text{ km}}{30 \text{ km/hr}} = \frac{80}{30} = \frac{8}{3} \text{ hours} \]

**Hint**: Use the same formula for time as you did for downstream speed.

6. **Convert Time to Hours and Minutes**:
To express \(\frac{8}{3}\) hours in hours and minutes:
\[ \frac{8}{3} \text{ hours} = 2 \text{ hours } + \frac{2}{3} \text{ hours} = 2 \text{ hours } + 40 \text{ minutes} \]

**Hint**: To convert a fraction of an hour to minutes, multiply by 60.

### Final Answer:
The time taken to cover the same distance upstream is **2 hours 40 minutes**.