Question

A motor boat whose speed is 18 km / h in still water takes 1hr more to go 24 km upstream than to return downstream to the same spot . find the speed of the stream (hint by making quadratic equation x^2+48x-324)

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Answer 1

Speed of boat =18km/hr

Distance =24km

Let x be the speed of stream.

Let t

1

and t

2

be the time for upstream and downstream.

As we know that,

speed=

time

distance

⇒time=

speed

distance

For upstream,

Speed =(18−x)km/hr

Distance =24km

Time =t

1

Therefore,

t

1

=

18−x

24

For downstream,

Speed =(18+x)km/hr

Distance =24km

Time =t

2

Therefore,

t

2

=

18+x

24

Now according to the question-

t

1

=t

2

+1

18−x

24

=

18+x

24

+1

⇒

18−x

1

−

18+x

1

=

24

1

⇒

(18−x)(18+x)

(18+x)−(18−x)

=

24

1

⇒48x=(18−x)(18+x)

⇒48x=324+18x−18x−x

2

⇒x

2

+48x−324=0

⇒x

2

+54x−6x−324=0

⇒x(x+54)−6(x+54)=0

⇒(x+54)(x−6)=0

⇒x=−54 or x=6

Since speed cannot be negative.

⇒x



=−54

∴x=6

Thus the speed of stream is 6km/hr

Hence the correct answer is 6km/hr.