a boat cover 32km upstream and 36km downstream in 7hr .also it covers 40 km upstream and 48km downstream in 9hr find the speed of the boat in still water and that of the speed of the stream
Answers
Answer:
Step-by-step explanation:
Let the speed of the boat
in still water = x kmph
Speed of the stream = y kmph
i ) relative speed of the
boat in downstream
= ( x + y ) kmph
Distance travelled = d1 = 36
Time = t1 hr
t1 = d1 / s1
t1 = 36/ ( x + y )
ii) relative speed of the boat
in upstream = ( x - y ) kmph
Distancw = d2 = 32 km
Time = t2
t2 = 32/ ( x - y )
Therefore ,
Total time = 7 hr
t1 + t2 = 7hr
36 / ( x + y ) + 32/ ( x - y ) = 7 ----( 1 )
iii) second time ,
Relativespeed of the boat in
downstream = ( x + y ) kmph
d3 = 48 km
Time = t3
t3 = 48/ ( x + y )
iv ) in upstream
Relative speed of the boat = ( x - y )
kmph
time = t4 hr
d4 = 40km
t4 = 40/ ( x - y )
Total time = 9 hr
48 / ( x + y ) + 40/ ( x - y ) = 9 ---( 2 )
Let 1 / ( x + y ) = a ,
1 / ( x - y ) = b
Then rewrite ( 1 ) and ( 2 ) we get
36 a + 32 b = 7 -----( 3 )
48a + 40b = 9 ------( 4 )
Multiply ( 4 ) with 4 and equation ( 3 ) with 5 and
192a + 160b = 36 ---( 5 )
180a + 160b = 35 -----( 6 )
Subtract ( 6 ) from ( 5 )
we get
a = 1/ 12
put a = 1/ 12 in ( 3 )
we get ,
b = 1/ 8
Now 1/ ( x + y ) = 1/ 12
1/ ( x - y ) = 1/ 8
Therefore ,
x + y = 12 ----( 7 )
x - y = 8 ----- ( 8 )
add ( 7 ) and ( 8 )
2x = 20
x = 10
put x = 10 in ( 7 ) we get
y = 2
Speed of the boat in
still water = x = 10 kmph
speed of the stream
= y = 2kmph