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 stre​

Answer 1

Answer:

the correct answer is 6km/hr.

Step-by-step explanation:

Given:-

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.

Answer 2

Let the speed of the stream be x km\hr.

The speed of the boat upstream = (18 - x) km/hr

The speed of the boat downstream = (18 + x) km/hr

Distance = 24 km

As given in the question,

Time for upstream = 1 + Time for downstream

24/(18 - x) = 1 + 24/(18 + x)

24/(18 - x) - 24/(18 + x) = 1

x2 + 48x - 324 = 0

(x + 54)(x - 6) = 0

x ≠ - 54 as speed cannot be negative.

x = 6

The speed of the stream = 6 km/hr