A boat goes 30 km upstream and 44 km downstream in 10 hours... in 13 hours it can go 40 km upstream and 55 km downstream .find the speed of the stream and that of boat in still water.
Answers
Answer:
Let the speed of boat in still water=x km\hr and The speed of stream=y km\hr
Speed of boat at downstream
⇒(x+y)km/hr
Speed of boat at upstream⇒(x−y)km/hr
∵time=
speed
distance
Time taken to cover 30 km upstream ⇒
x−y
30
Time taken to cover 44 km downstream⇒
x+y
44
According to the first condition,
⇒
x−y
30
=
x+y
44
=10
Time taken to cover 40 km upstream ⇒
x−y
40
Time taken to cover 55 km downstream ⇒
x+y
55
According to the second condition,
⇒
x−y
40
=
x+y
55
=13
Let
x−y
1
=uand
x+y
1
=v⇒30u+44v=10.....eq1
⇒40u+55v=13.....eq2
Multiplying eq1 by 3 and eq2 by 5 and subtract both
⇒(150u+220v=50)−(160u+220v=52)
⇒−10u=−2⇒u=
5
1
put u=
5
1
in eq1
⇒30×
5
1
+44v=10⇒44v=4⇒v=
4
1
⇒u=
x−y
1
=
5
1
⇒x−y=5...eq3⇒
v=
x+y
1
=
11
1
⇒x+y=11...eq4Subtracting eq3 and eq4, we get
⇒x=8
Put x=8 in eq3
⇒y=3
Hence, the speed of the boat in still water=8km\hr
The speed of stream=3km\hr
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