A boatman rows his boat 35 km upstream and 55 km downstream in 12 hours. He can row
30 km upstream and 44 km downstream in 10 hours. Find the speed of the stream and that of
the boat in still water. Hence, find the total time taken by the boatman to row 50 km upstream
and 77 km downstream.
Answers
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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
I hope this helps you.