Question

A boat goes 30km upstream and 44km downstream in 1 hour. The same boat goes
40km upstream and 53 km downstream in 13 hours. Determine the speed of stream
and that of boat in still water.​

Answer 1

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