a moter boat whose speed is 18km/he in still water takes 1he more to go to 24km upstream than to return downstream to same spot. find speed of stream
Answers
Answer:
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:
Speed of stream =6km/h
Step-by-step explanation:
Given:-
Speed of boat =18km/hr
Distance =24km
Let x be the speed of stream.
Let t and T be the time for upstream and downstream
Speed=Distance/Time
Time=Distance/Speed
For upstream,
Speed =(18−x)km/hr
Distance =24km
t=24/18-x
For downstream,
Speed =(18+x)km/hr
Distance =24km
T=24/18+x
t=T+1
24/18-x=(24/18+x)+1
(1/18-x)-(1/18+x)=1/24
(18+x)-(18-x)/(18-x)(18+x)
48x=(18−x)(18+x)
48x=324+18x−18x−x²
x²+48x−324=0
x²+54x−6x−324=0
x(x+54)−6(x+54)=0
(x+54)(x−6)=0
x=6km/h