A boat, while going downstream in a river covered a distance of 50 mile at an average speed of 60 miles per hour. While returning, because of the water resistance, it took one hour fifteen minutes to cover the same distance . What was the average speed of the boat during the whole journey?

Options

A. 40mph
B. 48mph
C. 50mph
D. 55mph

Answer

To find the average speed of the boat during the whole journey, we can follow these steps:

### Step 1: Calculate the time taken to go downstream
The distance covered downstream is 50 miles, and the average speed is 60 miles per hour.

Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
we can calculate the time taken downstream:
\[ \text{Time}_{\text{downstream}} = \frac{50 \text{ miles}}{60 \text{ miles/hour}} = \frac{5}{6} \text{ hours} \approx 0.833 \text{ hours} \]

### Step 2: Convert the return time to hours
The time taken to return upstream is given as 1 hour 15 minutes. We need to convert this into hours:
\[ 1 \text{ hour} + 15 \text{ minutes} = 1 + \frac{15}{60} = 1.25 \text{ hours} \]

### Step 3: Calculate the upstream speed
Now, we can find the speed of the boat while going upstream using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values:
\[ \text{Speed}_{\text{upstream}} = \frac{50 \text{ miles}}{1.25 \text{ hours}} = 40 \text{ miles/hour} \]

### Step 4: Calculate the average speed for the whole journey
The average speed for the entire journey can be calculated using the formula:
\[ \text{Average Speed} = \frac{2xy}{x + y} \]
where \(x\) is the downstream speed and \(y\) is the upstream speed. Substituting the values:
\[ x = 60 \text{ miles/hour}, \quad y = 40 \text{ miles/hour} \]
\[ \text{Average Speed} = \frac{2 \times 60 \times 40}{60 + 40} = \frac{4800}{100} = 48 \text{ miles/hour} \]

### Final Answer
The average speed of the boat during the whole journey is **48 miles per hour**.

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