The distance covered upstream in T hours by a boat is equal to the distance covered downstream in (T-1) hours. The speed of the boat upstream is 16 `km//hr` and that downstream is 20 `km//hr`. What is the distance covered by the boat downstream? (in km)

Options

A. 80
B. 120
C. 72
D. 85

Answer

To solve the problem, we need to find the distance covered by the boat downstream. Let's break it down step by step.

### Step 1: Understand the given information
- Speed of the boat upstream = 16 km/hr
- Speed of the boat downstream = 20 km/hr
- Time taken upstream = T hours
- Time taken downstream = (T - 1) hours

### Step 2: Write the distance formulas
The distance covered by the boat can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

#### Distance covered upstream:
Using the upstream speed and time:
\[ \text{Distance}_{\text{upstream}} = 16 \times T \]

#### Distance covered downstream:
Using the downstream speed and time:
\[ \text{Distance}_{\text{downstream}} = 20 \times (T - 1) \]

### Step 3: Set the distances equal
According to the problem, the distance covered upstream is equal to the distance covered downstream:
\[ 16T = 20(T - 1) \]

### Step 4: Solve the equation
Expanding the right side:
\[ 16T = 20T - 20 \]

Now, rearranging the equation:
\[ 16T - 20T = -20 \]
\[ -4T = -20 \]

Dividing both sides by -4:
\[ T = 5 \]

### Step 5: Calculate the distance downstream
Now that we have the value of T, we can find the distance covered downstream:
\[ \text{Distance}_{\text{downstream}} = 20 \times (T - 1) \]
Substituting T = 5:
\[ \text{Distance}_{\text{downstream}} = 20 \times (5 - 1) \]
\[ \text{Distance}_{\text{downstream}} = 20 \times 4 \]
\[ \text{Distance}_{\text{downstream}} = 80 \, \text{km} \]

### Final Answer
The distance covered by the boat downstream is **80 km**.

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