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.
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Answers
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.
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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.
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