A boat covers a distance of 30 km upstream and 44 km downstream in 10 hour . In 13 hours it cover a distance of 40 km upstream and 55 km downstream.find the speed of the boat in still water and that of stream
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...eq4
Subtracting 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