S.2 Applications of Simulyaneous Linear Equations

x + y = (60/72)(60) = 50km/h ----- 1
y - x = (60/120)(60) = 30km/h ----- 2

1 + 2

x+y+y-x = 50 + 30
2y = 80
y = 40 ----- 3

sub 3 into 1

x + 40 = 50
x = 50 - 40 =10

therefore
the speed of the stream is 10km/h
the speed of boat in still water is 40km/h

-----

驗算

(40-10)km/h in 120minutes
= (30km/h)(2h)
= 60km

(40+10)km/h in 72minutes
= (50km/h)(72/60)h
= (3600/60) km
= 60km

According to yhr question

The speed of the boat when travels in the upstream
=y-x

The speed of the boat when travels in the downstream
=y+x

So we have
2(y-x)=(72/60)(y+x) [distance=speed*time]
2y-2x=1.2y+1.2x
0.8y=3.2x
y=4x

Substitute into
2(y-x)=60
x=10

So y=40

the speed of the stream is 10 km/h and that of the boat in still water is 40 km/h