14. A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16km upstream
and 24km downstream in 7 hours. Find the speed of the boat in still water and the speed of the
stream.
Answers
Answer:
the answer to your question is in the attachment
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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.