1. A boat goes 10km upstream and 40km downstream in 8 hours. It can go 16km upstream and 32km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.
Answers
Step-by-step explanation:
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.