Question

23) The boat goes 30km upstream and 44km downstream in 10hours. In 13 hours, it can go
40km upstream and 55km downstream. Determine the
speed of stream and that of the boat
in still water.​

Answer 1

Answer:

stream speed be x

still water speed be y

downstream speed = x+y

upstream Speed =x-y

time = distance / speed

in first case

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

in second case

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

Let 1/x+y = u , 1/x-y = v

10 = 44u + 30v - 1

13 = 55 u + 40v - 2

multiple eq 1 by 4 and eq 2. by 3

40 = 176u + 120v

39 = 165u + 120v

by subtracting eq 1 and 2

1 = 11u

u= 1/11

put u=1/11 in eq1

10=44u + 30v

10 = 44×1/11 +30v

10 = 4+30v

6/30=v

1/5 = v

1/x+y = u

1/x+y =1/11

11=x+y -3

1/x-y =v

1/x-y=1/5

5 = x-y. -4

by adding eq 3 and 4

11 = x+y

5 =x-y

x = 8

put x =8 in eq 4

5=x+y

5 = 8+y

-3 = y