Boat A covers distance of 117km upstream in 9 hours, boat B covers distance of 135 km downstream in same time. If the speed of the stream is 2 km per hour (same for both the boats), How much more distance will boat A cover downstream then that boat B upstream in 30 hours

Options

A. 150km
B. 160km
C. 60km
D. 180km

Answer

To solve the problem step by step, we need to find the distances covered by both boats A and B under different conditions and then determine how much more distance boat A covers downstream compared to boat B upstream in 30 hours.

### Step 1: Calculate the Speed of Boat A
Boat A covers 117 km upstream in 9 hours. The speed of the stream is 2 km/h.

Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Let \( v_A \) be the speed of boat A. The effective speed of boat A upstream is:
\[ v_A - 2 = \frac{117}{9} \]

Calculating the right side:
\[ \frac{117}{9} = 13 \text{ km/h} \]

So, we have:
\[ v_A - 2 = 13 \]
\[ v_A = 13 + 2 = 15 \text{ km/h} \]

### Step 2: Calculate the Speed of Boat B
Boat B covers 135 km downstream in 9 hours. The effective speed of boat B downstream is:
\[ v_B + 2 = \frac{135}{9} \]

Calculating the right side:
\[ \frac{135}{9} = 15 \text{ km/h} \]

So, we have:
\[ v_B + 2 = 15 \]
\[ v_B = 15 - 2 = 13 \text{ km/h} \]

### Step 3: Calculate Distance Covered by Boat A Downstream in 30 Hours
Now, we need to calculate the distance covered by boat A downstream in 30 hours. The effective speed downstream is:
\[ v_A + 2 = 15 + 2 = 17 \text{ km/h} \]

Using the distance formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
\[ \text{Distance} = 17 \times 30 = 510 \text{ km} \]

### Step 4: Calculate Distance Covered by Boat B Upstream in 30 Hours
Next, we calculate the distance covered by boat B upstream in 30 hours. The effective speed upstream is:
\[ v_B - 2 = 13 - 2 = 11 \text{ km/h} \]

Using the distance formula again:
\[ \text{Distance} = 11 \times 30 = 330 \text{ km} \]

### Step 5: Calculate the Difference in Distances
Now, we find out how much more distance boat A covers downstream than boat B covers upstream:
\[ \text{Difference} = \text{Distance covered by A} - \text{Distance covered by B} \]
\[ \text{Difference} = 510 - 330 = 180 \text{ km} \]

### Final Answer
Boat A covers 180 km more downstream than boat B upstream in 30 hours.

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