Question

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

Answer 1

Step-by-step explanation:

ANSWER

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= timedistance

⇒time= speeddistance

For upstream,

Speed =(18−x)km/hr

Distance =24km

Time =t 1

Therefore,

t 1 = 18−x24

For downstream,

Speed =(18+x)km/hr

Distance =24km

Time =t 2

Therefore,t 2 = 18+x24

Now according to the question-

t 1 =t 2+118−x24

= 18+x2+1

⇒ 18−x1− 18+x1= 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

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