A boat covers 60 km downstream in 4 hours and 36 km upstream in the same time. What is the distance covered downstream by another boat (with speed in still water 18 km/hr) in the same stream in 2 hours? (in km)

Options

A. 84
B. 42
C. 66
D. 64

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the speed of the first boat downstream
The first boat covers 60 km downstream in 4 hours.
- Speed downstream = Distance / Time
- Speed downstream = 60 km / 4 hours = 15 km/hr.

### Step 2: Determine the speed of the first boat upstream
The first boat covers 36 km upstream in the same time (4 hours).
- Speed upstream = Distance / Time
- Speed upstream = 36 km / 4 hours = 9 km/hr.

### Step 3: Set up equations for the speed of the first boat in still water and the speed of the stream
Let:
- Speed of the first boat in still water = X1 km/hr
- Speed of the stream = Y km/hr

From the speeds calculated:
1. Downstream speed: X1 + Y = 15 (Equation 1)
2. Upstream speed: X1 - Y = 9 (Equation 2)

### Step 4: Solve the equations to find the speed of the stream
We can subtract Equation 2 from Equation 1:
- (X1 + Y) - (X1 - Y) = 15 - 9
- This simplifies to: 2Y = 6
- Therefore, Y = 6 / 2 = 3 km/hr.

### Step 5: Determine the speed of the second boat downstream
The speed of the second boat in still water is given as 18 km/hr.
- The downstream speed of the second boat = Speed of the second boat + Speed of the stream
- Downstream speed = 18 km/hr + 3 km/hr = 21 km/hr.

### Step 6: Calculate the distance covered by the second boat downstream in 2 hours
Distance = Speed × Time
- Distance = 21 km/hr × 2 hours = 42 km.

### Final Answer
The distance covered downstream by the second boat in 2 hours is **42 km**.

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