Question

# A motor boat whose speed is 18 Km/h in still water takes 1 hour more to go 24 Km upstream than to return downstream to the same spot. Find the speed of the stream.

Solution

## Given:- Speed of boat $$= 18 \; {km}/{hr}$$Distance $$= 24 \; km$$Let $$x$$ be the speed of stream.Let $${t}_{1}$$ and $${t}_{2}$$ be the time for upstream and downstream.As we know that,$$\text{speed} = \cfrac{\text{distance}}{\text{time}}$$$$\Rightarrow \text{time} = \cfrac{\text{distance}}{\text{speed}}$$For upstream,Speed $$= \left( 18 - x \right) \; {km}/{hr}$$Distance $$= 24 \; km$$Time $$= {t}_{1}$$Therefore,$${t}_{1} = \cfrac{24}{18 - x}$$For downstream,Speed $$= \left( 18 + x \right) \; {km}/{hr}$$Distance $$= 24 \; km$$Time $$= {t}_{2}$$Therefore,$${t}_{2} = \cfrac{24}{18 + x}$$Now according to the question-$${t}_{1} = {t}_{2} + 1$$$$\cfrac{24}{18 - x} = \cfrac{24}{18 + x} + 1$$$$\Rightarrow \cfrac{1}{18 - x} - \cfrac{1}{18 + x} = \cfrac{1}{24}$$$$\Rightarrow \cfrac{\left( 18 + x \right) - \left( 18 - x \right)}{\left( 18 - x \right) \left( 18 + x \right)} = \cfrac{1}{24}$$$$\Rightarrow 48x = \left( 18 - x \right) \left( 18 + x \right)$$$$\Rightarrow 48x = 324 + 18x - 18x - {x}^{2}$$$$\Rightarrow {x}^{2} + 48x - 324 = 0$$$$\Rightarrow {x}^{2} + 54x - 6x - 324 = 0$$$$\Rightarrow x \left( x + 54 \right) - 6 \left( x + 54 \right) = 0$$$$\Rightarrow \left( x + 54 \right) \left( x - 6 \right) = 0$$$$\Rightarrow x = -54 \text{ or } x = 6$$Since speed cannot be negative.$$\Rightarrow x \ne -54$$$$\therefore x = 6$$Thus the speed of stream is $$6 \; {km}/{hr}$$Hence the correct answer is $$6 \; {km}/{hr}$$.Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More