Question

A boat goes 16km upstream &24km downstream in 16 hrs.Also it covers 12km upstream & 36km downstream in the same time. Find the speed of the boat upstream and downstream.

Answer 1

speed of boat=xkm/h
speed of stream=ykm/h
speed of boat in down stream=(x+y)km/h
speed of boat in up stream=(x-y)km/h

we know,
t=d/s

case 1,
down stream
 t1=24/(x+y)
  
 upstream
t2=16/(x-y)

t1+t2=16
24/(x+y)+16/(x-y)=16

let 1/(x+y)=m 1/(x-y)=n
then,
24m+16n=16
= 3m=2n=2


case 2

downstream
t3=36/(x+y)
upstream t4=12/(x-y)
t3+t4=16
36m+12n=16
=9m+3n=4

now take lcm of 2n and 3n
then,18m=6n=8..........(1)
9m+6n=6..........(2)
sub 2 from 1
we get 9m=2
m=2/9
sub m in 2
9*2/9+6n=6
n=2/3

2/9=1/x+y
2x+2y=9..........3
2/3=1/x-y
2x-2y=3...................4

solve 3 nd 4
now, 4x=12
x=3

and...
y=3/2






hope its right............


 

Answer 2

Step-by-step explanation:

hope it will help you.....