Question

9. A motor boat can travel 30km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of boat in still water and the speed of the stream.

Answer 1

 let the speed of the boat be x and the speed of stream be y

30/x-y + 28/x+y =7

21/x-y + 21/x+y=5

therefore 1/x-y=a,1/x+y=b

30a+28b=7...1*21

21a+21b=5.....2*30

630a+588b=147

630a+630b=150

1-2

-42b=-3

b=1/14

substituting the value of b in 1

a=1/6

a=1/x-y

1/6=1/x-y

x-y=6....3

b=1/x+y

1/14=1/x+y

x+y=14......4

3+4

2x=20

x=10

x+y=14

y=14-10=4

therefore speed of boat is 10km/hr and speed of stream is 4km/hr