Question

) A motor boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km

upstream and 32 km downstream in the same time. Find the speed of the boat in still water

and the speed of the stream.

41) If the zeroes of the polynomial​

Answer 1

Answer:

HI MATE!!!

HERE IS THE SOLUTION

Step-by-step explanation:

Let

Speed of the boat in still water be xkm/hr

Speed of the stream be ykm/hr

Speed of boat in downstream = (x+y)km/hr

Speed of boat in upstream = xy)km/hr

According to given problem

Time taken to cover 12km upstream =

x−y

12

hrs

Time taken to cover 40km downstream =

x+y

40

hrs

But, the total time taken =8hr

=

x−y

12

+

x+y

40

hrs=8.........(1)

Time taken to cover 16km upstream =

x−y

16

hrs

Time taken to cover 32km downstream =

x+y

32

hrs

Total time taken = 8hr

=

x−y

16

+

x+y

32

hrs=8.......(2)

Put

x−y

1

=pand

x+y

1

=q

hence we get equation

12p + 40q = 8....(3)

16p + 32q = 8....(4)

Furthur simplyfying the eq we get

3p + 10q = 2..........(3)

2p + 4q = 1.........(4)

Multiply eq (3) by 2 and eq (4) by 3

6p + 20q = 4...........(3)

6p + 12q = 3............(4)

subtracting eq (4) from eq(3) we get

q=

8

1

and we get p=

4

1

Hencep=

x−y

1

=

4

1

andq=

x+y

1

=

8

1

x-y = 4..(5)

x+y= 8....(6)

Solving equation(5) and (6) we get x = 6 and y=2

Hence speed of boat in still water =6km/hr and speed of stream 2km/hr.