Question

18, A boat can row a certain distance in still water in 35 minutes. Same boat can row the same distance downstream in 12 minutes less than it can row in upstream. How long would boat take to row down with the stream.​

Answer 1

Answer:

23 mins.

Step-by-step explanation:

Boat rows in still water= 35mins.

in down stream it taken 20 minutes less

then, the boat will take = 35-12

= 23 mins.

Answer 2

Final Answer:

The time that the boat would take to row down with the stream is 30 minutes.

Given:

The boat rows a certain distance in still water in 35 minutes.

The same boat rows the same distance downstream in 12 minutes less than it can row in upstream.

To Find:

The time that the boat would take to row down with the stream is to be calculated.$s$

Explanation:

The concepts that are applicable here are as follows.

• The upstream speed of the boat is the difference between the speed of the boat in still water and the speed of the stream.
• The downstream speed of the boat is the sum of the speed of the boat in still water and the speed of the stream.

Step 1 of 5

As per the statement given in the problem, assume the following.

• The speed of the boat in still water is $b$ metres/min.
• The speed of the stream is $s$ metres/min.

Using the above information, derive the following.

• The upstream speed of the boat is $(b-s)$ metres/min.
• The downstream speed of the boat is $(b+s)$ metres/min.

Step 2 of 5

In continuation with the above calculations, the distance covered by the boat in still water is

$d=35b\;\;\;\;...(i)$

Again from the given statement, write the following equation.

$\frac{d}{b-s} -\frac{d}{b+s} =12\;\;\;\;(ii)$

Step 3 of 5

Solve the equation (ii) and apply the equation (i) in the following way.

$\\\frac{2sd}{b^2-s^2}=12\\ 6b^2-6s^2=sd=35bs \;\;\;\;[from\; eqn\;(i)]\\6b^2-36bs+bs-6s^2=0\\(6b+s)(b-6s)=0\\b-6s=0\;\;\;\;[6b\ne-s]\\b=6s\;\;\;\;(iii)$

Step 4 of 5

Write the following ratio from the equation (iii).

$\frac{b}{6} =\frac{s}{1} =k\;(say)\\\\b=6k\\s=k$

Putting these values of b and s in the equation (ii), the following is derived.

$\frac{d}{6k-k} -\frac{d}{6k+k}=12\\\\\frac{d}{5k}-\frac{d}{7k}=12\\\\\frac{d(7k-5k)}{35k}=12\\\\\frac{d\times 2k}{35k}=12\\\\d=6\times35=210\;m$

Step 5 of 5

Putting these values of d in the equation (i), the following is derived.

$b=6\;m/min$.

It implies that

$k=\frac{b}{6} =\frac{6}{6}=1\\s=1\;m/min$

So, the time that the boat takes to row down with the stream is

$=\frac{d}{b+s}\\\\=\frac{210}{6+1}\\\\=30\;mins$

Therefore, the required correct answer is the time duration of 30 minutes.

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