Question

A boat goes 12km upstrem and 40km downstrem in 8hrs.It can go 16km upstrem and 32km downsyrem in the same time .find the speed of the boat in still water and speed of the stream​

Answer 1

Answer:

Step-by-step explanation:

let the speed of stream is xkm/hr

speed of boat in still water is y km/hr

upstream means, opposite to the stream

downstream means, along the stream

so,

speed of the boat upstream = y-x km/hr

speed of the boat downstream = y+x km/hr

distance = speed × time

time = distance/speed

12/(y-x) + 40/(y+x) = 8 ........1

16/(y-x) + 32/(y+x) = 8  ........2

see eq.1

3/(y-x) + 10/(y+x) = 2

see eq2

2/(y-x) + 4/(y+x) = 1

let 1/(y-x) = a

and 1/(y+x) = b

3a + 10b = 2 ............3

2a + 4b = 1   ............4

multiplying eq3 by 2 and eq.4 by 3

6a + 20b = 4

6a + 12b = 2

subtracting we get

8b = 1

b=1/8

2a + 4/8 = 1

2a = 1- 1/2

a=1/4

now,

1/y-x = 1/4

y-x = 4

1/y+x = 1/8

y+x = 8

adding these two equations

2y = 12

y=6

x=2

so. speed of stream is 2km/hr

speed of boat in stil water 6km/hr