Question

a Boat takes 6 hours to travel 16 km upstream and 24 km downstream and it takes 13 hours to travel 36 km upstream and 48 km downstream find the speed of the boat in still water and the speed of the stream, by using two variables

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Answer 1

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Answer 2

Step-by-step explanation:

Let speed of boat in still water be ukm/hr

Let Speed of stream be vkm/hr

Upstream Speed=(u−v)km/hr

Downstream Speed(u+v)km/hr

u−v

16

+

u+v

24

=6

⇒

u

2

−v

2

16u+16v+24u−24v

=6

⇒

u

2

−v

2

40u−8v

=6⟶(i)

⇒

u−v

36

+

u+v

48

=13

=

u

2

−v

2

36u+36v+48u−48v

=13

⇒

u

2

−v

2

84u−12v

=13⟶(ii)

(i)÷(ii)

=

84u−12v

40u−8v

=

13

6

520u−104v=504u−72v

16u=32v

u=2v

Putting u=2v in equation(i)

(2v)

2

−v

2

40(2v)−8v

=6

3v

2

80v−8v

=6

72=18v

v=4km/hr

u=8km/hr