Ariv can row his boat 36 km downstream and 32 km in 7 hours. moreover he can row his boat 48 km downstream and 40 km upstream in 9 hours. find the speed of ariv's boat in still water and in flow of the stream.
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Answer:
x=10km/ph y=2km/ph
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