Question

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

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Answer 1

Time taken by boat to row downstream is 30 minutes.

Given:

• A boat can row a certain distance in still water in 35 minutes.
• The same boat can row the same distance downstream in 12 minutes less than it can row in upstream.

To find:

• How long would the boat take to row down with the stream.

Solution:

Formula/Concept to be used:

• $Speed = \frac{Distance}{Time}$
• If the speed of the boat in still water is 'x' m/min and the speed of the stream is 'y' m/min.
• Speed of boat upstream $=( x - y)$m/min
• Speed of boat downstream$= (x + y)$m/min

Step 1:

Write the equations.

Let the distance travelled by boat is 'd' meter.

$x = \frac{d}{35}$

$\bf d = 35x...eq1$

ATQ,

$\bf \frac{d}{x - y} - \frac{d}{x + y} = 12...eq2$

$\frac{dx + dy - dx + dy}{ {x}^{2} - {y}^{2} } = 12$

$\frac{2yd}{ {x}^{2} - {y}^{2} } = 12$

Put the value from eq1.

$\frac{2 \times y(35x)}{ {x}^{2} - {y}^{2} } = 12$

$35xy = 6 {x}^{2} - 6 {y}^{2}$

$\bf 6 {x}^{2} - 35xy - 6 {y}^{2} = 0$

Step 2:

Factorise the equation.

$6 {x}^{2} - 36xy+xy - 6 {y}^{2} = 0$

$6x(x - 6y) + y(x - 6y) = 0$

$(6x + y)(x - 6y) = 0$

$6x + y = 0$

$6x \neq - y$

or

$x - 6y = 0$

$\bf x = 6y$

or

$\bf \frac{x}{y} = \frac{6}{1}=k ...eq3$

Step 3:

Put the value of eq3 in eq2.

$\frac{d}{5k} - \frac{d}{7k} = 12$

$\frac{7dk - 5dk}{35 {k}} = 12$

$\frac{2d}{35} = 12$

$\bf d = 210$ meter

Step 4:

Find the time taken by boat to row downstream.

Speed of boat in still water $210 = 35x$

$x = \frac{210}{35}$

$\bf x = 6$m/min

Because $\bf x = 6y$

so, put value of x.

$6 = 6y$

$\bf y = 1$m/min

Time taken by the boat to row downstream $= \frac{210}{6+1}$

Time taken by the boat to row downstream$= 30 \: minutes$

Thus,

Time taken by boat to row downstream is 30 minutes.

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