Question

1. A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream. 

Answer 1

Let the speed of boat upstream be x and downstream be y.
acc to the question;
since
speed=distance/time
therefore;
time =distance/speed
12/x+40/y=8hrs.
=12y+40x=8xy----(i)(taking L.C/M and then shifting the denominator to R.H.S)
If it can go 16 km upstream and 32 km downstream in the same time;
therefore;
16/x+32/y=8hrs
=16y+32x=8xy---(ii)(taking L.C/M and then shifting the denominator to R.H.S)
therefore (i)=(ii)
i.e.,
12y+40x=16y+32x
40x-32x=16y-12y
8x=4y
y=2x
substituting y=2x in eqn (ii)
16(2x)+32x=8(x)(2x)
64x=16x²
64=16x
x=64/16
x=4
therefore ;
from eqn(ii)
16y+32(4)=8(4)y
16y+128=32y
128=32y-16y
16y=128
y=8
hope i helped u:)