In the UK pedestrians will never have a green light while cars have a green light and the timings wait until pedestrians will have finished crossing before allowing cars. There might be some slow walkers or people who crossed without green (it's dangerous but not illegal) but everything is done to ensure neither pedestrians nor cars are told to go while the other isn't told to stop.

I think this might be the reason for the strength disparity. Tasks that require strong people tend to be more dangerous but a sensible tribe leader would send the strongest to do these tasks whether they are male or female. A tribe where the strength balance leans female will grow slower than a tribe where there is equal distribution which will grow slower than one with male balance. This selection effect would cause evolution in that direction.

Just stick some wings and big engines on the side of a rail car. We could call it the aerotrain!