The ratio of the speeds of a motorboat to that of the current of water is 17:9. The boat goes along with the current in 4hr 32 min. It will come back in:

Options

A. 16hr 48 min
B. 14hr 44 min
C. 15hr 16 min
D. 12hr 48 min

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the speeds of the boat and the current
Let the speed of the motorboat be \( x \) km/h and the speed of the current be \( y \) km/h. According to the problem, the ratio of the speeds is given as:
\[ \frac{x}{y} = \frac{17}{9} \]
This implies:
\[ x = 17k \quad \text{and} \quad y = 9k \]
for some constant \( k \).

### Step 2: Calculate the downstream speed
When the boat is going downstream (with the current), its effective speed is:
\[ \text{Downstream speed} = x + y = 17k + 9k = 26k \text{ km/h} \]

### Step 3: Convert the time taken downstream into hours
The time taken to go downstream is given as 4 hours 32 minutes. We need to convert this into hours:
\[ 4 \text{ hours } 32 \text{ minutes} = 4 + \frac{32}{60} = 4 + \frac{8}{15} = \frac{60 + 8}{15} = \frac{68}{15} \text{ hours} \]

### Step 4: Use the formula for distance
The distance traveled downstream can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Thus, the distance \( d \) is:
\[ d = 26k \times \frac{68}{15} \]

### Step 5: Calculate the upstream speed
When the boat is coming back upstream (against the current), its effective speed is:
\[ \text{Upstream speed} = x - y = 17k - 9k = 8k \text{ km/h} \]

### Step 6: Calculate the time taken to return upstream
Using the same distance \( d \), the time taken to return upstream can be calculated as:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{d}{8k} \]
Substituting \( d \):
\[ \text{Time} = \frac{26k \times \frac{68}{15}}{8k} = \frac{26 \times \frac{68}{15}}{8} = \frac{26 \times 68}{15 \times 8} \]
Calculating this gives:
\[ = \frac{1768}{120} = \frac{441}{30} \text{ hours} \]

### Step 7: Convert the time back to hours and minutes
Now, we convert \( \frac{441}{30} \) hours into hours and minutes:
\[ \frac{441}{30} = 14.7 \text{ hours} \]
This means 14 hours and \( 0.7 \times 60 = 42 \) minutes.

### Final Answer
The boat will take 14 hours and 42 minutes to come back upstream.

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