A boat covers 143 km upstream in 13 hours and the same distance downstream in 11 hours. What is the speed (in km / hr ) of the boat in still (without stream) water?

Question:A boat covers 143 km upstream in 13 hours and the same distance downstream in 11 hours. What is the speed (in km/hr) of the boat in still (without stream) water?

Choices:

• 8 km/hr

• 10 km/hr

• 12 km/hr

• 14 km/hr

Correct Answer: 12 km/hr

Detailed Solution:

To determine the speed of the boat in still water, we denote the speed of the boat in still water as \(B\) km/hr and the speed of the stream as \(S\) km/hr. For upstream, the effective speed of the boat will be reduced due to the current, which gives us a speed of \(B - S\) km/hr. For downstream, the current aids the boat, making the effective speed \(B + S\) km/hr.

From the problem statement, we have:

• Distance covered upstream = 143 km

• Time taken upstream = 13 hours

• Distance covered downstream = 143 km

• Time taken downstream = 11 hours

We can write two equations for the two scenarios (upstream and downstream):

$\[ \frac{143}{B - S} = 13 \quad \text{(1)} \] \[ $\frac{143}{B + S} = 11 \quad \text{(2)} \]

Solving equation (1) for \(B - S\):

$\[ B - S = \frac{143}{13} = 11 \quad \text{(3)} \]$

Solving equation (2) for \(B + S\):

$\[ B + S = \frac{143}{11} = 13 \quad \text{(4)} \]$

Now we have two linear equations:

$\[ B - S = 11 \quad \text{(3)} \] \[ B + S = 13 \quad \text{(4)} \]$

We can solve these equations simultaneously by adding (3) and (4):

$\[ (B - S) + (B + S) = 11 + 13 \] \[ 2B = 24 \] \[ B = \frac{24}{2} = 12 \quad \text{km/hr} \]$

Thus, the speed of the boat in still water is 12 km/hr, which is the correct answer.