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 that remained the speed of the boat in still water
Answers
Answer:
the speed of the boat in still water=8km\hr
The speed of stream=3km\hr
Step-by-step explanation:
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