If the speed of a boat in still water is 13 km/h and speed of stream is 9 km/h then find the total time taken by boat to cover 88 km downstream and 22 km upstream.

Options

A. 9.5 hours
B. 10.5 hours
C. 7.5 hours
D. 12.5 hours

Answer

To solve the problem of finding the total time taken by a boat to cover 88 km downstream and 22 km upstream, we can follow these steps:

### Step 1: Identify the speeds
- Speed of the boat in still water (x) = 13 km/h
- Speed of the stream (y) = 9 km/h

### Step 2: Calculate downstream speed
The speed of the boat downstream is the sum of the speed of the boat in still water and the speed of the stream:
\[ \text{Downstream speed} = x + y = 13 + 9 = 22 \text{ km/h} \]

### Step 3: Calculate time taken to cover 88 km downstream
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
For downstream:
\[ t_1 = \frac{88 \text{ km}}{22 \text{ km/h}} = 4 \text{ hours} \]

### Step 4: Calculate upstream speed
The speed of the boat upstream is the difference between the speed of the boat in still water and the speed of the stream:
\[ \text{Upstream speed} = x - y = 13 - 9 = 4 \text{ km/h} \]

### Step 5: Calculate time taken to cover 22 km upstream
Using the same time formula:
\[ t_2 = \frac{22 \text{ km}}{4 \text{ km/h}} = 5.5 \text{ hours} \]

### Step 6: Calculate total time taken
The total time taken by the boat to cover both distances is the sum of the time taken downstream and the time taken upstream:
\[ \text{Total time} = t_1 + t_2 = 4 \text{ hours} + 5.5 \text{ hours} = 9.5 \text{ hours} \]

### Final Answer
The total time taken by the boat to cover 88 km downstream and 22 km upstream is **9.5 hours**.

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