NRICH Weekly Problem

Solution to last week's NRICH problem

Weekly Problem 7 - 2013

Stage: 3 

Alternate angles BDF and DFG are equal, so lines BD and FG are parallel.
Therefore angle BCA = angle FGC = 80∘ (corresponding angles).

Consider triangle ABC: x+70+80=180 so x=30.

Can you do this week's?

Weekly Problem 8 - 2013

Stage: 3 

I walk to the bike shop at 3 miles per hour and cycle back along the same route at 12 miles per hour. What is my average speed in miles per hour, for the time I am actually travelling on the route?