The boat covers 32 km upstream and 36 km downstream in 7hour also it covers 40 km upstream in 9hours. The speed of the boat in still water is
Answers
Answer:
Let the speed of the boat in still water be x km/hr and the speed of the stream but y km/hr. Then,
Speed upstream =(x−y)km/hr
Speed downstream =(x+y) km/hr
Now, Time taken to cover 32km upstream =
x−y
32
hrs
Time taken to cover 36 km downstream =
x+y
36
hrs
But, total time of journey is 7 hours.
∴
x−y
32
+
x+y
36
=7 ..(i)
Time taken to cover 40km upstream =
x−y
40
Time taken to cover 48 km downstream =
x+y
48
In this case, total time of journey is given to be 9 hours.
∴
x−y
40
+
x+y
48
=9 (ii)
Putting
x−y
1
=u and
x+y
1
=v in equations (i) and (ii), we get
32u+36v=7⇒32u−36v−7=0 ..(iii)
40u+48v=9⇒40u−48v−9=0 ..(iv)
Solving these equations by cross-multiplication, we get
36×−9−48×−7
u
=
32×−9−40×−7
−v
=
32×48−40×36
1
⇒
−324+336
u
=
−288+280
−v
=
1536−1440
1
⇒
12
u
=
8
v
=
96
1
⇒u=
96
12
and v=
96
8
⇒u=
8
1
and v=
12
1
Now, u=
8
1
⇒
x−y
1
=
8
1
⇒x−y=8 ..(v)
and, v=
12
1
⇒
x+y
1
=
12
1
⇒x+y=12 ..(vi)
Solving equations (v) and (vi), we get x=10 and y=2
Hence, Speed of the boat in still water =10 km/hr
and Speed of the stream =2km/hr.
Step-by-step explanation:
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