Our group consists of three members: Dimitra, Maximos and Xenofontas.

This is our first challenge and it is addressed to spanish group 4

Enjoy!

1st Challenge από Vagelis lamprou

Hello! This is our second challenge which is addressed to spanish group 5

Enjoy!

2nd Challenge από Vagelis lamprou

This is the solution to the 1st challenge:

S= U₁*t₁
S= U₂*t₂
The total S'=U*(t₁+t₂)= U(S/U₁+S/U₂)=U*[(SU₁+SU₂)/U₁*U₂)]=U[S(U₁+U₂)/U₁*U₂]
But the total S' is also equal with 2S, so
2S=U[S(U₁+U₂)/U₁*U₂]<=>

U=2S*U₁*U₂/S(U₁+U₂)<=>

U=2U₁U₂/U₁+U₂<=>

U=2*20*30/20+30=1200/50=24m/s
 

This is the solution to the 2nd challenge:

The triangles ADE and DEZ have common base DE, so the ratio of their areas is equal with the ratio of their heights, so A'D'/D'B'=4/2

From Thales Theorem: AD/DB=4/2 so AD/AB=4/6=2/3

Because the triangles ADE, ABC are simiral, the ratio of their areas is eqyal with the square of similarity's ratio.

So (ADE)/(ABC)=(2/3)^2= 4/9, so (ABC)=9/4(ADE)= 9/4*4= 9