Question

a boat goes 30km upstream and 44 km downstream 10hr. in 13hr it can go 40km upstream and 55km downstream determine the speed of boat and that the boat stil in water

Answer 1

let rate upstream = x km/hr
and rate downstream = y km/hr.
⇒40/x +55/y = 13...(i)
and 30/x +44/y = 10
after multiplying (ii) by 4 and (i) by 3 and subtracting we will get 11/y = 1 or y = 11.
Substituting y = 11 in (i)
⇒we get: x = 5.
∴rate in still water =1/2(11+5) kmph = 8 kmph.
∴rate of current=1/2(11-5)kmph = 3 kmph

Answer 2

Answer:

Speed of boat=8 km/hr

Speed of stream =3 km/hr

Step-by-step explanation:

Upstream =x-y

Downstream =x+y

(30/x-y)+(44/x+y)=10

(40/x-y)+(55/x+y)=13

Let 1/x-y=a

1/x+y=b

30a+44b=10=>15a+22b=5-----(1)

40a+55b=13------(2)

(1)=>b=(5-15/22)-------(3)

(3) in (2)

40a+55(5-15a/22)=13

(80a+25-75a/2)=13

5a=1

a=1/5

b=(5-15(1/5)/22)

b=2/22=1/11

b=1/11

X-y=5

X+y=11

2x=16

X=8

8-y=5

-y=-3

Y=3